What is the greatest common factor of 45 and 165?

Factors of 45 are 1, 3, 5, 9, 15 and 45.

Factors of 165 are 1, 3, 5, 11, 15, 33, 55 and 165.

It is clear that 15 is the greatest common factor.

Alternate method:

Expressing each number as the product of prime numbers can simplify the problem easily.

Prime factorization of 45 = 3x3x5

Prime factorization of 165 = 3x5x11.

From the P.F. of both numbers it is clear that 3x5 = 15 is common.

So, Greatest common factor is 15.
the GCF is 15