Best Answer

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.

Q: 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?

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3x

10t

The GCF is 7c.

Simplification using the greatest common factor does.Simplification using the greatest common factor does.Simplification using the greatest common factor does.Simplification using the greatest common factor does.

The prime factors of 21 are 3 and 7.The prime factors of 14 are 2 and 7.The greatest common factor of 21 and 14 is 7.21ab and 14b also have another factor in common - b. So, the greatest common factor of 21ab and 14b would appear to be 7b . However, it is possible that a and 14 share a common factor of 2, in which case the greatest common factor of 21ab and 14b would be 14b.In summary, if a is an even number (i.e. having a factor of 2), the greatest common factor is 14b.If a is not an even number, the greatest common factor is 7b.gcf(21ab, 14b) = 7b.

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