Factors

In general, a factor is any of the numbers that can be multiplied together to create another number.  But, the definition changes a little according to what kind of math you're doing.

For whole numbers a and n:

We say a is a factor of n if ab = n for some whole number b.

For example, 3 is a factor of 21, since 3 · 7 = 21.

But 4 is not a factor of 21, since there is no whole number b for which 4b = 21.

For polynomials p and r:

We say p is a factor of r if pq = r for some polynomial r.

For example, x + 1 is a factor of x² – 2x – 3, since

(x + 1)(x – 3) = x² – 2x – 3.

But x + 2 is not a factor of x² – 2x – 3, since there is no polynomial q for which (x + 2)(q) = x² – 2x – 3.

Common Factors

If two numbers (or polynomials) have a factor in common, then it is called a common factor.

For instance, the numbers 15 and 33 have 3 as a common factor.

The polynomials

4x + 4  and  x² – 2x – 3

have x + 1 as a common factor.