"Factoring" involves finding the numbers or "factors" you multiply to get another number. For instance, the factors of 15 are 3 and 5, because 3x5=15. Some numbers have more than one factorization (way of being factored). For instance, 12 can be factored as 1x12, 2x6, or 3x4. A number that can be only factored as 1 times itself is called "prime". The first few primes are 2,3,5,7,11,13. The number 1 is not regarded as a prime, and is usually not included in factorizations because 1 goes in to everything.

You most often want to find the "prime factorization" of a number. That is, you usually want to find the list of all the prime-number factors of a given number. The prime factorization does not include 1, but does include every copy of every prime factor. For instance, the prime factorization of 8 is 2x2x2, not just "2".

There are at least 2 ways that you can find the prime factors of a number or an expression.

Method

Explanation

1. Finding the prime factorization of 24.

Going from top to bottom,
Divide 24 by 2 = 12
Divide 12 by 2 = 6
Divide 6 by 2 = 3
So the prime factorization of
24 is 2 x 2 x 2 x 3

2. Finding the prime factorization of x² - 4x -5.

In order to factor x² -4x - 5, you can use a 4-box.
The four individual squares must add up to x² -4x - 5.
The length and width of the box will be our factors.

Factoring"Factoring" involves finding the numbers or "factors" you multiply to get another number. For instance, the factors of 15 are 3 and 5, because 3x5=15. Some numbers have more than one factorization (way of being factored). For instance, 12 can be factored as 1x12, 2x6, or 3x4. A number that can be only factored as 1 times itself is called "prime". The first few primes are 2,3,5,7,11,13. The number 1 is not regarded as a prime, and is usually not included in factorizations because 1 goes in to everything.

## Table of Contents

You most often want to find the "prime factorization" of a number. That is, you usually want to find the list of all the prime-number factors of a given number. The prime factorization does not include 1, but does include every copy of every prime factor. For instance, the prime factorization of 8 is 2x2x2, not just "2".

There are at least 2 ways that you can find the prime factors of a number or an expression.

Method

Explanation

Divide 24 by 2 = 12

Divide 12 by 2 = 6

Divide 6 by 2 = 3

So the prime factorization of

24 is

2 x 2 x 2 x 3The four individual squares must add up to x² -4x - 5.

The length and width of the box will be our factors.

Further Discussion