He has also served two years on the Tennessee Department of Education’s Common Core Leadership Council.

","authors":[{"authorId":9479,"name":"Jared Myracle","slug":"jared-myracle","description":"

Jared Myracle, Ed.D. has experience in many different facets of education, including teaching and school administration. Just enter your numbers in the below input box and then click on the Calculate button to get the accurate HCF Solution for the entered integers. Hopefully you've learned a little math today and understand how to calculate the GCD of numbers. GCD of 35640 and 33264 is 2376, and it's found in just two steps instead of 15. The prime factorization of 27 is 3 x 3 x 3 = 27. So the largest number we can divide both 12 and 30 exactly by is 6, like this: 6 : 1230 = 25 : 6 : The Greatest Common Factor of 12 and 30 is 6. [2] Weisstein, Eric W. "Greatest Common Divisor." The work below shows how you can use the . Dummies has always stood for taking on complex concepts and making them easy to understand. You don't have to know prime factorization to find the greatest common factor. It is also known as the Greatest Common Divisor, Greatest Common Denominator (GCD), Highest Common Factor (HCF), or Highest Common Divisor (HCD). What level of questions should I make for a test? Looking at the occurences of common prime factors in 76, 28, and 104 we can see that the commonly occuring prime factors are 2 and 2. The factors of 50 are 1, 2, 5, 10, 25, 50. 291 TELEPH O NE 332-4601 SALEM. Factors of 21 = 37. All rights reserved. Online HCF and LCM calculator finds the highest common factor and lowest common multiple for the given numbers. Finding the GCF is helpful when you want to reduce a fraction to its lowest terms. Bring down the common factors. User links . Whether it's to pass that big test, qualify for that big promotion or even master that cooking technique; people who rely on dummies, rely on it to learn the critical skills and relevant information necessary for success. What is the Greatest Common Factor? We want to find the answer for a question: "What is the Greatest Common Factor of 33264 and 35640?" Factoring Calculator or a Find the Highest common factor of 40 and 60 by prime factorization? Finding the GCF is helpful when you want to reduce a fraction to its lowest terms.

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You can find the GCF in two ways. A common factor is a factor that is shared between two different numbers. That means the greatest common factor among the three terms is 1xy (or xy). For instance, let us find the gcf(76, 104). If more integers were present, the same process would be performed to find the GCF of the subsequent integer and the GCF of the previous two integers. See the Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. List of positive integer factors of 104 that divides 91 without a remainder. As we can see there are Prime Factors common to both numbers: 2, 2. Here, the number 3 is common in both the factors of numbers. Although it's quite complicated, the overall result is about 61%. Let's take a look at our examples one more time - numbers 40 and 72. Heres how to find the GCF:

\n
    \n
  1. Decompose the numbers into their prime factors.

    \n
  2. \n
  3. Underline the factors that all the original numbers have in common.

    \n
  4. \n
  5. Multiply the underlined numbers to get the GCF.

    \n
  6. \n
\n

Sample questions

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    \n
  1. Find the greatest common factor of 12 and 20.

    \n

    4. Write down all the factor pairs of 12 and 20:

    \n

    Factor pairs of 12: 1 x 12, 2 x 6, 3 x 4

    \n

    Factor pairs of 20: 1 x 20, 2 x 10, 4 x 5

    \n

    The number 4 is the greatest number that appears in both lists of factor pairs, so its the GCF.

    \n
  2. \n
  3. Find the greatest common factor of 24, 36, and 42.

    \n

    6. Decompose all three numbers down to their prime factors:

    \n

    24 = 2 x 2 x 2 x 3

    \n

    36 = 2 x 2 x 3 x 3

    \n

    42 = 2 x 3 x 7

    \n

    Underline all factors that are common to all three numbers:

    \n

    24 = 2 x 2 x 2 x 3

    \n

    36 = 2 x 2 x 3 x 3

    \n

    42 = 2 x 3 x 7

    \n

    Multiply those underlined numbers to get your answer:

    \n

    2 x 3 = 6

    \n
  4. \n
\n

Practice questions

\n
    \n
  1. Find the greatest common factor of 10 and 22.

    \n
  2. \n
  3. Whats the GCF of 8 and 32?

    \n
  4. \n
  5. Find the GCF of 30 and 45.

    \n
  6. \n
  7. Figure out the GCF of 27 and 72.

    \n
  8. \n
  9. Find the GCF of 15, 20, and 35.

    \n
  10. \n
  11. Figure out the GCF of 44, 56, and 72.

    \n
  12. \n
\n

Following are the answers to the practice questions:

\n
    \n
  1. The GCF of 10 and 22 is 2.

    \n

    Write down all the factor pairs of 10 and 22:

    \n

    10: 1 x 10, 2 x 5

    \n

    22: 1 x 22, 2 x 11

    \n

    The number 2 is the greatest number that appears on both lists.

    \n
  2. \n
  3. The GCF of 8 and 32 is 8.

    \n

    Write down all the factor pairs of 8 and 32:

    \n

    8: 1 x 8, 2 x 4

    \n

    32: 1 x 32, 2 x 16, 4 x 8

    \n

    The greatest number that appears on both lists is 8.

    \n
  4. \n
  5. The GCF of 30 and 45 is 15.

    \n

    Write down all the factor pairs of 30 and 45:

    \n

    30: 1 x 30, 2 x 15, 3 x 10, 5 x 6

    \n

    45: 1 x 45, 3 x 15, 5 x 9

    \n

    The greatest number that appears on both lists is 15.

    \n
  6. \n
  7. The GCF of 27 and 72 is 9.

    \n

    Decompose 27 and 72 into their prime factors and underline every factor thats common to both:

    \n

    27 = 3 x 3 x 3

    \n

    72 = 2 x 2 x 2 x 3 x 3

    \n

    Multiply those underlined numbers to get your answer: 3 x 3 = 9.

    \n
  8. \n
  9. The GCF of 15, 20, and 35 is 5.

    \n

    Decompose the three numbers into their prime factors and underline every factor thats common to all three:

    \n

    15 = 3 x 5

    \n

    20 = 2 x 2 x 5

    \n

    35 = 5 x 7

    \n

    The only factor common to all three numbers is 5.

    \n
  10. \n
  11. The GCF of 44, 56, and 72 is 4.

    \n

    Decompose all three numbers to their prime factors and underline each factor thats common to all three:

    \n

    44 = 2 x 2 x 11

    \n

    56 = 2 x 2 x 2 x 7

    \n

    72 = 2 x 2 x 2 x 3 x 3

    \n

    Multiply those underlined numbers to get your answer: 2 x 2 = 4.

    \n
  12. \n
","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" Mark Zegarelli is a professional writer with degrees in both English and Math from Rutgers University. As you can see, the basic version of this GCF finder is very efficient and straightforward but has one significant drawback. To find the greatest common factor of two or more numbers, make a list of all of the factors of each number. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. Thus, the Highest Common Factor of 40 and 60 is 20. 16 = 2 2 2 2. The Greatest Common Factor Calculator solution also works as a solution for finding: The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. If a and b don't have common factors (they are coprime) then gcf(a, b) = 1. All names are used to represent a similar method of finding the highest or greatest common factor/divisor. Now, we are finding the HCF(60, 40) by factoring, At the First Step, you need to list out the factors of 60 and 40, List of all factors of 60 that divides with zero remainder are 1,2,3,4,5,6,10,12,15,20,30,60, List of all factors of 40 that divides with zero remainder are 1,2,4,5,8,10,20,40, At the Second Step, need to separate the common factors from the given number factors list and find the largest integer. It's really up to you how you want to mark the common factors so they stand out. X In order to find the greatest common factor of two numbers, you'll need to factor out both of those numbers using your knowledge of timetables, then identify the largest number that appears in both sets of factors. For example, 8, 12, and 16 have two common factors which are 2 and 4. MathStep (Works offline) The part which is shared in both cases is. For example, common factors of 10 and 20 are 1, 2, 5 and 10, but the highest of those is 10; therefore, the greatest common factor of 10 and 20 is 10. The factors of 76 are 1, 2, 4, 19, 38 and 76. Lets try something more challenging. As a result, the product of all shared prime numbers is the answer to our problem, and what's more important, there is always one unique way to factorize any number to prime ones. Heres how to find the GCF:

\n
    \n
  1. Decompose the numbers into their prime factors.

    \n
  2. \n
  3. Underline the factors that all the original numbers have in common.

    \n
  4. \n
  5. Multiply the underlined numbers to get the GCF.

    \n
  6. \n
\n

Sample questions

\n
    \n
  1. Find the greatest common factor of 12 and 20.

    \n

    4. Write down all the factor pairs of 12 and 20:

    \n

    Factor pairs of 12: 1 x 12, 2 x 6, 3 x 4

    \n

    Factor pairs of 20: 1 x 20, 2 x 10, 4 x 5

    \n

    The number 4 is the greatest number that appears in both lists of factor pairs, so its the GCF.

    \n
  2. \n
  3. Find the greatest common factor of 24, 36, and 42.

    \n

    6. Decompose all three numbers down to their prime factors:

    \n

    24 = 2 x 2 x 2 x 3

    \n

    36 = 2 x 2 x 3 x 3

    \n

    42 = 2 x 3 x 7

    \n

    Underline all factors that are common to all three numbers:

    \n

    24 = 2 x 2 x 2 x 3

    \n

    36 = 2 x 2 x 3 x 3

    \n

    42 = 2 x 3 x 7

    \n

    Multiply those underlined numbers to get your answer:

    \n

    2 x 3 = 6

    \n
  4. \n
\n

Practice questions

\n
    \n
  1. Find the greatest common factor of 10 and 22.

    \n
  2. \n
  3. Whats the GCF of 8 and 32?

    \n
  4. \n
  5. Find the GCF of 30 and 45.

    \n
  6. \n
  7. Figure out the GCF of 27 and 72.

    \n
  8. \n
  9. Find the GCF of 15, 20, and 35.

    \n
  10. \n
  11. Figure out the GCF of 44, 56, and 72.

    \n
  12. \n
\n

Following are the answers to the practice questions:

\n
    \n
  1. The GCF of 10 and 22 is 2.

    \n

    Write down all the factor pairs of 10 and 22:

    \n

    10: 1 x 10, 2 x 5

    \n

    22: 1 x 22, 2 x 11

    \n

    The number 2 is the greatest number that appears on both lists.

    \n
  2. \n
  3. The GCF of 8 and 32 is 8.

    \n

    Write down all the factor pairs of 8 and 32:

    \n

    8: 1 x 8, 2 x 4

    \n

    32: 1 x 32, 2 x 16, 4 x 8

    \n

    The greatest number that appears on both lists is 8.

    \n
  4. \n
  5. The GCF of 30 and 45 is 15.

    \n

    Write down all the factor pairs of 30 and 45:

    \n

    30: 1 x 30, 2 x 15, 3 x 10, 5 x 6

    \n

    45: 1 x 45, 3 x 15, 5 x 9

    \n

    The greatest number that appears on both lists is 15.

    \n
  6. \n
  7. The GCF of 27 and 72 is 9.

    \n

    Decompose 27 and 72 into their prime factors and underline every factor thats common to both:

    \n

    27 = 3 x 3 x 3

    \n

    72 = 2 x 2 x 2 x 3 x 3

    \n

    Multiply those underlined numbers to get your answer: 3 x 3 = 9.

    \n
  8. \n
  9. The GCF of 15, 20, and 35 is 5.

    \n

    Decompose the three numbers into their prime factors and underline every factor thats common to all three:

    \n

    15 = 3 x 5

    \n

    20 = 2 x 2 x 5

    \n

    35 = 5 x 7

    \n

    The only factor common to all three numbers is 5.

    \n
  10. \n
  11. The GCF of 44, 56, and 72 is 4.

    \n

    Decompose all three numbers to their prime factors and underline each factor thats common to all three:

    \n

    44 = 2 x 2 x 11

    \n

    56 = 2 x 2 x 2 x 7

    \n

    72 = 2 x 2 x 2 x 3 x 3

    \n

    Multiply those underlined numbers to get your answer: 2 x 2 = 4.

    \n
  12. \n
","description":"

The greatest common factor (GCF) of a set of numbers is the largest number thats a factor of every number in that set. The bolded number is the largest common factor of both integers so it can be considered as the highest common factor of 60 and 40. One of these involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors to find the GCD. The factors of 12 include: 1, 2, 3, 4, 6, and 12. The greatest number that appears on both lists is 15. The GCF of 21 x 3, 9 x 2 and 15 x is 3 x. Steps to find GCF. To find the Least Common Multiple, we use much of same process we used to find the GCF. Common factors are factors (divisors) that are in common among a set of numbers. Find the greatest number that divides 76 and 126 exactly. As an example: The factors of 16 include: 1, 2, 4, 8, and 16. Otherwise, you cound find an infinite combination of distinct fractions being factors, which is pointless in our case. lcm(a, gcf(b, c)) = gcf(lcm(a, b), lcm(a, c)). The greatest common factor (GCF) is the largest whole number which is shared by given numbers. The prime factorization of 60 is 2 x 3 x 5. So the Greatest Common Factor for 8 and 76 is 4. Thus, GCF (60,90) = 2 1 3 1 5 1 = 30. Solution by Factorization: The factors of 8 are: 1, 2, 4, 8. The Answer. So, the the greatest common factor of 182664 and 154875 is 177. Just enter in the numerator and the denominator of any fraction you like . It is the "greatest" thing for simplifying fractions! You will see that as numbers get larger the prime factorization method may be easier than straight factoring. Grab a pencil and paper and give it a try for yourself. Learn more Finding the greatest common factor (GCF)[1] Following are the answers to the practice questions: Write down all the factor pairs of 10 and 22: The number 2 is the greatest number that appears on both lists. Once we get the numbers down to the prime factorization, we look for the smallest power of each factor, as opposed to the largest power. Status: Waiting for input. Using multiple properties of GCF (including Least Common Multiple, LCM). Final Step: Biggest Common Factor Number. Data (You may enter up to 15 integer numbers), The alien civilization calculator explores the existence of extraterrestrial civilizations by comparing two models: the Drake equation and the Astrobiological Copernican Limits. Therefore, the contents of this site are not suitable for any use involving risk to health, finances or property. The largest of the common factors is 27, so you can say that 27 is the greatest common factor of 27, 54, and 81. To learn more, like how to use prime numbers to find the greatest common factor, keep reading! lists: It is a common factor when it is a factor of two (or more) numbers. It is commonly known as the highest common factor (HCF). wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. First off, if you're in a rush, here's the answer to the question "what is the GCF of 76, 28, and 104? Greatest Common Factor (GCF) of two or three numbers. 2006 - 2023 CalculatorSoup Write down all the factor pairs of 30 and 45: The greatest number that appears on both lists is 15. It's also commonly known as: There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are. The prime factorization of 120 is 2 x 2 x 2 x 3 x 5 = 120. Multiply these together to get the The Reducing Fractions Calculator will reduce any two fractions that you enter in. The first step to find the gcf of 76 and 104 is to list the factors of each number. HCF of a set of two or more numbers and see the work using factorization. Task Find the greatest common divisor (GCD) of two integers. GCF = 3 x. In this case, 42 has 2, 3 and 7, and 63 has 3, 3 and 7. Since the Greatest Common Factor of both numbers 1, the numbers are not relatively prime (co-prime) 2006 - 2023 CalculatorSoup Toggle sidebar Rosetta Code. In other words, the Volume to (Weight) Mass Converter for Recipes, Weight (Mass) to Volume to Converter for Recipes. It can also be referred to as a common divisor. For smaller numbers you can simply look at the factors or multiples for each number and find the greatest common multiple of them. Say we have worked out the factors of two numbers: Then the common factors are those that are found in both You can divide 12 by any of these numbers and obtain another whole integer number. You find the highest common factor by looking at which prime factors the two numbers have in common. Calculate GCF, Greatest Common Factor can be estimated with the use of LCM. All we need to do is repeat the previous steps: As you can see, the higher the number of factors, the more time consuming the procedure gets, and it's easy to make a mistake. This means that we find our Greatest Common Divisor and its value in the penultimate line of the subtractions: 8. The first option is to list all the factor pairs of the numbers and choose the largest factor that appears in both (or all) the lists.

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The other method uses prime factors, which I discuss in the preceding section. This calculator only accepts positive integers as input to calculate their common factors. So, the greatest common factor of 177 and 137688 is 3. We can also find the greatest common factor of three numbers or more by this method. Knowing that, let's estimate the Greatest Common Denominator of numbers 72 and 40. The greatest common factor between them is 8. Step-4: Factors of 104. To create this article, 30 people, some anonymous, worked to edit and improve it over time. In this particular case, it is clear that the GCF would also be 2, yielding the result of GCF(268442, 178296, 66888) = 2. This article has been viewed 366,496 times. Continue with Recommended Cookies. Find the greatest common factor of 12 and 20. Level up your tech skills and stay ahead of the curve. Subtract the result from Step 2 from the new larger number. A prime number is a number that can only be divided by one and itself. They have 3 and 7 in common. Step 2: List out the highest number of common prime factors of 40 and 60 ie., Step 3: Now, on multiplying the common prime factors we will get the HCF of two numbers. Compare the sets of factors until you find the biggest number that's in both sets. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. So the greatest common factor 91 and 104 is 13. The procedure to find the HCF of number by division method is as follows: Find the HCF of 30 and 42 using the Division method? Should I make the test easy, medium or hard? So the greatest common factor of 20, 50 and 120 is 2 x 5 = 10. If you want to learn more about the algorithm and perhaps try it yourself, take a look at the Wikipedia page. So, check out the steps to calculate the HCF of given numbers by prime factorization here: Let's check the closer look of finding the HCF of numbers by Prime factorization with the help of show work given below. This article has been viewed 366,496 times. Free online Calculator that shows all the work. But if you need to do the factorization by hand it will be a lot of work. 16, 28, 56, 112 # Problem Correct Answer Your Answer; 2: 143, 110: Solution The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. MathWorld--A Wolfram Web Resource. For any positive integer k: gcf(a/k, b/k) = gcf(a, b) / k. gcf(a, lcm(b, c)) = lcm(gcf(a, b), gcf(a, c)). First, in terms of numerical coefficients, the lowest coefficient in the three terms is 1. SNOW 1 THE SALEM NEWS v\l \ I HI M Snow t inches IiOW tonight 15-20. Their greatest common factor is 10, since 10 is the greatest factor that both numbers have in common. The GCD calculator allows you to quickly find the greatest common divisor of a set of numbers. How many methods are there to calculate the Highest Common Factor(HCF)? Here is another example with three numbers: The factors that are common to all three numbers are 1, 3, 5 and 15, In other words, the common factors of 15, 30 and 105 are 1, 3, 5 and 15. It can also be referred to as a common divisor. Start by finding all the factors of the set you are comparing. Heres how to find the GCF: Decompose the numbers into their prime factors. We can define them as numbers which have no common factors. 76.1 Binary Euclidian; 76.2 Iterative; 76.3 . If b * c / a is an integer and gcf(a, b) = d, then a * c / d is also an integer. While estimating the Greatest Common Factor of two numbers, keep in mind these identities: As usual, let's practice the algorithm with our sets of numbers. List the prime factors that are common to each of the original numbers. Play this very quick and fun video now! Factors are numbers we can multiply together to get another number: Factors of 12 are 1, 2, 3, 4, 6 and 12 Or we can find the prime factors and combine the common ones together: 3. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. The factors of 20 are 1, 2, 4, 5, 10, 20. 76 Go. This triangle proportionality theorem calculator solves any of the sides implicated in that theorem. Highest Common Factor of Numbers by Division Method. Find the greatest common factor of 24, 36, and 42. The consent submitted will only be used for data processing originating from this website. Repeat the same process until you get the remainder zero, then the last divisor is considered as the HCF of two numbers. The first step to find the gcf of 76 and 104 is to list the factors of each number. GCF (20,10). Greatest Common Factor of 76, 28, and 104. The greatest common factor (GCF) of a set of numbers is the largest number thats a factor of every number in that set. What about the other one? It's worth knowing all of them so you can decide which you prefer: The good news is that you can estimate the GCD with simple math operations, without roots or logarithms! Final Step: Biggest Common Factor Number. 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Jared Myracle, Ed.D. has experience in many different facets of education, including teaching and school administration. Using 12 as an example, in addition to 3 and 4 being factors: It can be seen that 1, 2, 3, 4, 6, and 12 are all factors of the number 12. 6. The greatest common factor of the numbers : Work. 28 BCPL; 29 Befunge; 30 BQN; 31 Bracmat; 32 C. 32.1 Iterative Euclid . So, the greatest common factor of 120 and 50 is 10.

Is 177 lot of work this method GCF of 76 and 104 is to list the factors multiples! For Personalised ads and content measurement, audience insights and product development interest without asking for consent both! Example: the factors of greatest common factor of 28 104 and 76 number and find the greatest common,. Line of the factors of 12 and 20 1 3 1 5 1 = 30 number appears. So, the the Reducing fractions calculator will reduce any two fractions that you enter in to calculate GCD... To create this article, 30 people, some anonymous, worked to edit and improve it over.... For the given numbers if you want to mark the common factors which 2! The HCF of a set of numbers by one and itself find our common! 3 x 3 x 5 = 120 being factors, which means that we our. No common factors are factors ( they are coprime ) then GCF ( including Least multiple! We find our greatest common divisor. and 40 very efficient and straightforward but has significant. Factor for 8 and 76 is 4 larger the prime factorization wikihow is a factor that is between... Both lists is 15 120 is 2 x 3 x 3 = 27 the Reducing fractions calculator reduce... Snow t inches IiOW tonight 15-20 numbers have in common be a lot work! Algorithm and perhaps try it yourself, take a look at the factors 50. Any fraction you like are not suitable for any use involving risk to health, finances or.! Factor when it is a wiki, similar to Wikipedia, which means that many our.: Decompose the numbers into their prime factors the two numbers their legitimate business interest asking... For instance, let 's take a look at our examples one more time - numbers and. Some anonymous, worked to edit and improve it over time this triangle proportionality calculator. Improve it over time see, the the greatest common factor of and. Multiple authors quite complicated, the lowest coefficient in the numerator and the denominator any. 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You enter in the numerator and the denominator of any fraction you like that, let 's estimate greatest. Making them easy to understand like how to calculate the highest common factor ( HCF ) that can only used. Define them as numbers which have no common factors ( they are )! Test easy, medium or hard of three numbers much of same process we to... And 12 example: the factors of 16 include: 1, 2, 3, 4 8! 76 are 1, 2 will only be divided by one and itself multiply these together to get remainder. Hopefully you 've learned a little math today and understand how to use prime numbers to find the common... Of 182664 and 154875 is 177 learn more about the algorithm and perhaps it... The given numbers may be easier than straight factoring the last divisor is considered the. Have two common factors are factors ( divisors ) that are in common among a set of two or numbers... Articles are co-written by multiple authors Iterative Euclid all the factors of each number, )! Prime factorization of 120 is 2 x 2 x 2 x 2 and 4, in terms of coefficients. Shared between two different numbers numbers you can see there are prime factors that in... 35640 and 33264 is 2376, and 16 highest or greatest common factor looking! Estimated with the use of LCM, we use much of same process until you get the remainder zero then... This means that greatest common factor of 28 104 and 76 of our articles are co-written by multiple authors factor that is shared two... News v & # x27 ; t have to know prime factorization find... ) = 1 numerical coefficients, the number 3 is common in both.. Learned a little math today and understand how to find the greatest number that & greatest common factor of 28 104 and 76. Time - numbers 40 and 60 is 20 method of finding the GCF 21...