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# What is the easiest way to find the greatest common factors of two integers?

Question #83172. Asked by Alsoco. (Jul 10 07 6:49 PM)

zbeckabee

If either number is negative, drop its negative sign.
If 'a' is smaller than 'b', then swap them so 'a' is greater than or equal to 'b'. This step is not strictly necessary, but it will help avoid one division step below.
If 'b' is zero, then the greatest common divisor is 'a'. We are now done. But...
If 'b' is not zero, then divide 'a' by 'b' and get the remainder.
Go back to step 3, using 'b' as the new 'a' value and the remainder from step 4 as the new 'b' value.

http://www.wikihow.com/Find-the-Greatest-Common-Divisor-(Gcd)-of-Two-Integers

 Jul 10 07, 7:09 PM
cae_16682

I don't know whether this is the easiest. But basically what we need to do is take the "prime factorization" of the number.

Prime factorization is basically : expressing a number as a product of prime numbers such as 2, 3, 5, 7, and so on.

http://en.wikipedia.org/wiki/List_of_prime_numbers#The_first_500_prime_numbers

So if I were to find the GCF of say 14, 28 and 42

Then the prime factorization of each of these numbers gives:

14 = 7 x 2
28 = 7 x 2 x 2
42 = 7 x 3 x 2

Taking a good look now at the factors of the thress numbers, you find that they all have one '7' and one '2' in common.

To find the GCF: You need to multiply the common factors (in this case 7 and 2)

So you get: GCF of 14, 28 and 42 is 7 x 2 = 14

The link below also gives a good example(s)

http://www.helpwithfractions.com/greatest-common-factor.html

 Jul 10 07, 7:12 PM

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The text passage contains a question about finding the greatest common factor of two integers, followed by two different methods to solve the problem, one of which includes an example with an answer.
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# What is the easiest way to find the greatest common factors of two integers?

Question #83172. Asked by Alsoco. (Jul 10 07 6:49 PM)

zbeckabee

If either number is negative, drop its negative sign.
If 'a' is smaller than 'b', then swap them so 'a' is greater than or equal to 'b'. This step is not strictly necessary, but it will help avoid one division step below.
If 'b' is zero, then the greatest common divisor is 'a'. We are now done. But...
If 'b' is not zero, then divide 'a' by 'b' and get the remainder.
Go back to step 3, using 'b' as the new 'a' value and the remainder from step 4 as the new 'b' value.

http://www.wikihow.com/Find-the-Greatest-Common-Divisor-(Gcd)-of-Two-Integers

 Jul 10 07, 7:09 PM
cae_16682

I don't know whether this is the easiest. But basically what we need to do is take the "prime factorization" of the number.

Prime factorization is basically : expressing a number as a product of prime numbers such as 2, 3, 5, 7, and so on.

http://en.wikipedia.org/wiki/List_of_prime_numbers#The_first_500_prime_numbers

So if I were to find the GCF of say 14, 28 and 42

Then the prime factorization of each of these numbers gives:

14 = 7 x 2
28 = 7 x 2 x 2
42 = 7 x 3 x 2

Taking a good look now at the factors of the thress numbers, you find that they all have one '7' and one '2' in common.

To find the GCF: You need to multiply the common factors (in this case 7 and 2)

So you get: GCF of 14, 28 and 42 is 7 x 2 = 14

The link below also gives a good example(s)

http://www.helpwithfractions.com/greatest-common-factor.html

 Jul 10 07, 7:12 PM

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"Ask FunTrivia" is for entertainment purposes only, and answers offered are unverified and unchecked by FunTrivia. We cannot guarantee the accuracy or veracity of ANY statement posted. Feel free to post an updated response if you feel that an answer is inadequate or incorrect. Please thoroughly research items where accuracy is important to you using multiple reliable sources. By accessing our website, you agree to be bound by our terms of service.
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The text passage contains a question about finding the greatest common factor of two integers, followed by two different methods to solve the problem, one of which includes an example with an answer.

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