Question

What is the common factor of
6mn⁴ + 18m⁵n² + 12m⁴n⁵ - 18mn³​

Answer 1

It is 6mn² if you want to know the greatest common factor.

Explanation:

Let me start with the coefficients. Since 6 can divide all coefficients, we should pick 6.

For the variables, the least power of m found in the expression is m¹ or simply m.

The least power of n found in the expression is n². Wrapping this up, you get 6mn².

But the expression has many common factors.

e.g. 2, 3, 6, m, n, n², . . .

You can also say -2, -3, -6, -m, -n, -n².

Generally, you may have many common factors, but you will have only one greatest common factor.