How do you factor using the gcf?

Answer 1

Suppose the greatest common factor of x and y is g where g is a positive integer.The x = g*p and y = g*q for some integers p and q.

Then one factorisation of (x + y) is g*(p + q). It is possible, of course, that (p + q) can be factorised further.

For example if x = 15, y = 21 so that x + y = 36

GCF(x, y) = 3

x = 3*5 and y = 3*7

so (x + y) = 36 can be factorised as 3*(5 + 7) = 3 * 12

But the 12 can be factorised into 2*2*3 so the full factorisation is 2*2*3*3.