Greatest Common Factor of 108 and 312
GCF(108, 312) = 12, Greatest common factor of 108 and 312 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 108 and 312. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 108 and 312 by prime factorization method
We will first find the prime factorization of 108 and 312.
Prime Factorization of 108 is 1, 2, 2, 3, 3, 3 and Prime Factorization of 312 is 1, 2, 2, 2, 3, 13.
- Factorize\( (108) = \) \(1\times 2\times 2\times 3\times 3\times 3\)
- Factorize\( (312) = \) \(1\times 2\times 2\times 2\times 3\times 13\)
Now we need to find any which are common for each number (1, 2, 2, 3) and multiply these numbers together.
\(GCF(108, 312) = 1\times 2\times 2\times 3 = 12\).
Greatest Common Factor of 108 and 312 by matching factors method
List of positive integers factors of 108 leaving a remainder zero is 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
List of positive integers factors of 312 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
As you can see, 12 is the greatest and common number that 108 and 312 divides into.
So the greatest common factor 108 and 312 is 12.
\(GCF(108, 312) = 12\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
