Greatest Common Factor of 132 and 9724
GCF(132, 9724) = 44, Greatest common factor of 132 and 9724 is 44. Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the numbers can be divided. There are two different methods to calculate Greatest Common Factor of 132 and 9724. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 132 and 9724 by prime factorization method
We will first find the prime factorization of 132 and 9724.
Prime Factorization of 132 is 1, 2, 2, 3, 11 and Prime Factorization of 9724 is 1, 2, 2, 11, 13, 17.
- Factorize\( (132) = \) \(1\times 2\times 2\times 3\times 11\)
- Factorize\( (9724) = \) \(1\times 2\times 2\times 11\times 13\times 17\)
Now we need to find any which are common for each number (1, 2, 2, 11) and multiply these numbers together.
\(GCF(132, 9724) = 1\times 2\times 2\times 11 = 44\).
Greatest Common Factor of 132 and 9724 by matching factors method
List of positive integers factors of 132 leaving a remainder zero is 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
List of positive integers factors of 9724 leaving a remainder zero is 1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724
As you can see, 44 is the greatest and common number that 132 and 9724 divides into.
So the greatest common factor 132 and 9724 is 44.
\(GCF(132, 9724) = 44\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
