Greatest Common Factor of 64 and 352
GCF(64, 352) = 32, Greatest common factor of 64 and 352 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 64 and 352. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 64 and 352 by prime factorization method
We will first find the prime factorization of 64 and 352.
Prime Factorization of 64 is 1, 2, 2, 2, 2, 2, 2 and Prime Factorization of 352 is 1, 2, 2, 2, 2, 2, 11.
- Factorize\( (64) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\)
- Factorize\( (352) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 11\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2, 2) and multiply these numbers together.
\(GCF(64, 352) = 1\times 2\times 2\times 2\times 2\times 2 = 32\).
Greatest Common Factor of 64 and 352 by matching factors method
List of positive integers factors of 64 leaving a remainder zero is 1, 2, 4, 8, 16, 32, 64
List of positive integers factors of 352 leaving a remainder zero is 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352
As you can see, 32 is the greatest and common number that 64 and 352 divides into.
So the greatest common factor 64 and 352 is 32.
\(GCF(64, 352) = 32\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
