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What are Factors?

A factor is a smaller number that divides exactly any larger number and gives the remainder zero. Here are some examples:

If we divide 6 by 2 , the remainder is 0. We say 6 is "exactly divisible" by 2 and call 2 a factor of 6.

6 is also exactly divisible by
1 , 2, 3 and 6.
So, 1, 2, 3 and 6 are
factors of 6.

6 is not "exactly divisible" by 4 and 5 and so 4 and 5 are not factors of 6.

More Examples of Finding Factors

Let's try another example showing how to find out what factors are. We will find all the factors of 12 by finding all the numbers that 12 can be exactly divided by.

12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1

12 is exactly divisible by 1, 2, 3, 4, 6 and 12. So 1, 2, 3, 4, 6 and 12 are the factors of 12.

Finding factors can be a bit "trial and error" - we start with 1 and work up. In this case 5, 7, 8, 9, 10 do not divide 12 exactly and are not factors.


In this example we will find all of the factors of 20.

20 ÷ 1 = 20
20 ÷ 2 = 10
20 ÷ 4 = 5
20 ÷ 5 = 4
20 ÷ 10 = 2
20 ÷ 20 = 1

20 is exactly divisible by 1, 2, 4, 5, 10 and 20. So 1, 2, 4, 5, 10 and 20 are the factors of 20 .

Hint: Look at the example above for finding all the factors of 20.

Notice that when we find the factor which is exactly half (10) we are pretty much finished our search since the only factor remaining to be found is the number (20) itself.

It's the same when finding the factors for all even numbers.

Factor Games

Try the game below for a little fun with factors:

Factors Worksheets

You might find this factor calculator external website icon handy for checking your answers.

 

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