Question

You need to find the GCF of 256 and 400 Would you rather list their factors or use the prime factorization

Answer 1

If you were looking for the greatest common factor, you'd want to see the list of their factors.

A prime factorization breaks it down as far as possible and as a result has as few high numbers as possible. If you want the number to be as great as possible, you would want to see the list of all the factors.

Answer 2

GCF of 256 and 400 is 16.

Explanation:

We have to find GCF that is the greatest common factor of 256 and 400.

We would use prime factorization that is breaking the number in the form of product of prime numbers. Then, in order to calculate greatest common factor, we multiply the common prime factors of both the numbers.

`256 = 2^8 = 2* 2* 2* 2* 2* 2* 2* 2\\400 = 2^4* 5^2 = 2* 2* 2* 2* 5* 5`

Common factor:

`256~ \&~ 400 = 2* 2* 2* 2 = 16`

Hence, GCF of 256 and 400 is 16.