Question

What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?

Answer 1

For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.

So, we have the following expressions:

$42a ^ 5b ^ 3\\35a ^ 3b ^ 4\\42ab ^ 4$

We look for the positive integers that divide to 35 and 42 without leaving residue:

42: 1,2,3,6,7,14,21

35: 1,5,7

Thus, the GCF of 42 and 35 is 7

Then, the GCF of the three expressions is:

$7ab ^ 3$

Answer:

$7ab ^ 3$