Question

How do you find the GCF of 21, 45?

Answer 1

GCF of 21 and 45 is 3

Explanation:

Consider that `45=9(5)` and `21=3(7)`

Since `3^2=9` we can say

`45=3^2(5)` 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(2)+3`

Then we can say

`45-=3 mod 21`

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