Greatest Common Factor of 96 and 32
GCF(96, 32) = 32, Greatest common factor of 96 and 32 is 32. 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 96 and 32. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 96 and 32 by prime factorization method
We will first find the prime factorization of 96 and 32.
Prime Factorization of 96 is 1, 2, 2, 2, 2, 2, 3 and Prime Factorization of 32 is 1, 2, 2, 2, 2, 2.
- Factorize\( (96) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 3\)
- Factorize\( (32) = \) \(1\times 2\times 2\times 2\times 2\times 2\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2, 2) and multiply these numbers together.
\(GCF(96, 32) = 1\times 2\times 2\times 2\times 2\times 2 = 32\).
Greatest Common Factor of 96 and 32 by matching factors method
List of positive integers factors of 96 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
List of positive integers factors of 32 leaving a remainder zero is 1, 2, 4, 8, 16, 32
As you can see, 32 is the greatest and common number that 96 and 32 divides into.
So the greatest common factor 96 and 32 is 32.
\(GCF(96, 32) = 32\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
