If the greatest common factor of a and b is 3 what values are possible for the greatest common factor of a squared and b?

Answer 1

a is 3m

b is 3n

m and n are relatively prime - they do not have any common factors.

a2 = 9m2

Since m had no factors in common with n, m2 also has no factors in common with n. We know that 3 is a common factor of a and b. The only new possible factor between a2 and b is the second 3 when a is squared. We do not know whether b had more than one factor of 3. So, the greatest common factor of a2 and b, when the greatest common factor of a and b is 3, is either 3 or 9.