Greatest Common Factor of 36 and 132
GCF(36, 132) = 12, Greatest common factor of 36 and 132 is 12. 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 36 and 132. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 36 and 132 by prime factorization method
We will first find the prime factorization of 36 and 132.
Prime Factorization of 36 is 1, 2, 2, 3, 3 and Prime Factorization of 132 is 1, 2, 2, 3, 11.
- Factorize\( (36) = \) \(1\times 2\times 2\times 3\times 3\)
- Factorize\( (132) = \) \(1\times 2\times 2\times 3\times 11\)
Now we need to find any which are common for each number (1, 2, 2, 3) and multiply these numbers together.
\(GCF(36, 132) = 1\times 2\times 2\times 3 = 12\).
Greatest Common Factor of 36 and 132 by matching factors method
List of positive integers factors of 36 leaving a remainder zero is 1, 2, 3, 4, 6, 9, 12, 18, 36
List of positive integers factors of 132 leaving a remainder zero is 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
As you can see, 12 is the greatest and common number that 36 and 132 divides into.
So the greatest common factor 36 and 132 is 12.
\(GCF(36, 132) = 12\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
