Factoring integers


Factoring integers is the easiest thing we can factor. It means to make the integer look like a multiplication problem by looking for its prime factorization






In other words, factor the integer until all factor are prime numbers

It is very important to know how to do this before learning how to find the greatest common factor and how to factor trinomials

Here is the algorithm:

When factoring, start by dividing the number by 2. Then, keep dividing any factor divisible by 2 that is not prime by 2 until no factors is divisible by 2.

When no factors are divisible by 2, start by dividing by 3 until no factors are divisible by 3.

When no factors are divisible by 3, start by dividing by 4 until.....

and so forth...

Let us start practicing!

Factor 4

Dividing 4 by 2 gives 2, so

4 = 2 * 2

Factor 12

Dividing 12 by 2 gives 6, so

12 = 2 * 6

However, 6 is a factor divisible by 2, so factor 6

factoring 6 gives 2 * 3

Putting it all together,

12 = 2 * 6 = 2 * 2 * 3

when factoring integers a problem can get complicated when the number is big. when this happens make a tree as the following example demonstrates. We call this a factor tree

Factor 72

Factor tree of 72


Pulling out all factors inside the red shape that looks like a golf bat, we get:

72 = 2 * 2 * 2 * 3 * 3

Factor tree of 240


Once again, pulling out all factors inside the red shape that looks like a golf bat, we get:



240 = 2 * 2 * 2 * 2 * 3 * 5

You should notice tough that 72 and 240 can be factored faster than that if you know your multiplication table.

72 = 8 * 9

8 = 2 * 2 * 2 and 9 = 3 * 3

So, 72 = 2 * 2 * 2 * 3 * 3

240 = 24 * 10

10 = 2 * 5 and 24 = 4 * 6 = 2 * 2 * 2 * 3

So, 240 = 2 * 2 * 2 * 2 * 3 * 5





Recent Articles

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz