The Largest One

The GCF must be the greatest common factor, not just any common factor. The terms of 8x + 20 share a 2, and 8x + 20 = 2(4x + 10) is true. But look inside the parentheses. The terms 4x and 10 still share another 2. The factoring is finished only when the terms inside share nothing: 8x + 20 = 4(2x + 5).

A smaller common factor gives a true equation, but the factoring is not complete. For example, 2(4x + 10) = 2 × 2(2x + 5) = 4(2x + 5). If you take out the GCF 4 at the start, you do not need this second step.

To test whether you are finished, look at the terms inside the parentheses. If any number or letter still divides all of them, the factor you took out was not the greatest. An expression with a common factor still inside is not in factored form.