# How do you find the GCF of 21, 45?

Jan 20, 2017

GCF of 21 and 45 is 3

#### Explanation:

Consider that $45 = 9 \left(5\right)$ and $21 = 3 \left(7\right)$

Since ${3}^{2} = 9$ we can say

$45 = {3}^{2} \left(5\right)$ Therefore 45 is divisible by 3

Since both 45 and 21 are divisible by 3 it is a common factor. Also, since 3 is the only common factor between the two numbers in their prime factorization; it is the greatest common factor of 45 and 21.

Or GCF (21,45)=3.

Another method

Since $45 = 21 \left(2\right) + 3$

Then we can say

$45 \equiv 3 \mod 21$

Since 3 is prime GCF (21,45)=3