How do you find the GCF of 21, 45?

1 Answer
Jan 20, 2017

Answer:

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