Become a math whiz with AI Tutoring, Practice Questions & more.

HotmathMath Homework. Do It Faster, Learn It Better.

# Factors

As we start to get into division, we''ll start hearing the word "factors" very often. But what exactly is a factor? how is this concept related to division? What do we need to know about factors? Let''s find out:

## Factors defined

Factors are like smaller building blocks of numbers. When we multiply them, we get the original number that we broke down into smaller parts.

For example, 5 is a factor of 10, since we can multiply 5 by 2 to get 10. But 2 is also a factor of 10 since we can multiply 2 by 5 to get 10.

Aside from 1 and 10, there are no other factors for the number 10. We can''t use numbers like 3.33 and 3 because factors must be a whole number.

The term "factor" takes on a slightly more complex meaning when we''re dealing with polynomials.

Consider the following:

x+1
is a factor of
x2-2x-3

Why?

Because we can do this:
(x+1)(x-3) = x2-2x-3

In other words,
x+1
is a smaller piece of the larger polynomial equation, and when it is multiplied by another polynomial
(x-3)
, it results in the original polynomial
x^2-2x-3

## Common factors

Common factors can be very important in math.

We can look at two different numbers and determine if they have common factors. For example:

4x+4
and
x2-2x-3
have x+1 as a common factor.
4x+4= 4(x+1)

and
x2-2x-3 =(x+1)(x-3)

## Topics related to the Factors

Irreducible Polynomials

Factoring: a ≠ 1

## Flashcards covering the Factors

Common Core: 4th Grade Math Flashcards

## Practice tests covering the Factors

Common Core: 4th Grade Math Diagnostic Tests