How to Factor Numbers

How to Factor Numbers

“Factors” are the numbers we multiply to get another number. In this post learn how to factor numbers easily.

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Step by step guide to factoring numbers

  • Factoring numbers means breaking the numbers into their prime factors.
  • First few prime numbers: \(2, 3, 5, 7, 11, 13, 17, 19\)
  • To factor a number, start with the smallest prime number which is \(2\). Is the number divisible by \(2\)? If so, divide it by \(2\) and do the same for the result. If not, check the next prime number which is \(3\), and do the same process.

Factoring Numbers – Example 1:

List all positive factors of \(8\).

Solution:

Write the upside-down division: \(8\) is divisible by \(2\). Then:

8 2
4 2
2 2
1  

The first column shows all the factors of number \(8\).
Then: \(8=2 \ \times \ 2 \ \times \ 2\) or \(8=2^{3}\)

All factors of \(8\) are: \(1, 2, 4, 8\)

Factoring Numbers – Example 2:

List all positive factors of \(24\).

Solution:

Write the upside-down division: 

24 2
12 2
6 2
3 3
1

The second column is the answer.
Then: \(24= 2 \ \times \ 2 \ \times \ 2 \ \times \ 3\)
or \(24=2^{3} \ \times \ 3\)

All factors of \(24\) are: \(1, 2, 3, 4, 6, 8, 12, and 24\)

Factoring Numbers – Example 3:

List all positive factors of \(12\).

Solution:

Write the upside-down division:

12 2
6 2
3 3
1  

The second column is the answer.
Then: \(12=2×2×3\)
or \(12=2^2×3\)

All factors of \(12\) are: \(1, 2, 3, 4, 6, 12\)

Factoring Numbers – Example 4:

List all positive factors of \(20\).

Solution:

Write the upside-down division:

20 2
10 2
5 5
1  

Write the upside-down division:
The second column is the answer.
Then: \(20=2×2×5\) or \(20=2^2×5\)

All factors of \(20\) are: \(1, 2, 4, 5, 10, and 20\)

Exercises for Factoring Numbers –

List all positive factors of each number.

  1. \(\color{blue}{68}\)
  2. \(\color{blue}{56}\)
  3. \(\color{blue}{24}\)
  4. \(\color{blue}{40}\)
  5. \(\color{blue}{86}\)
  6. \(\color{blue}{78}\)

Download Factoring Numbers Worksheet

  1. \(\color{blue}{1, 2, 4, 17, 34, 68}\)
  2. \(\color{blue}{1, 2, 4, 7, 8, 14, 28, 56}\)
  3. \(\color{blue}{1, 2, 3, 4, 6, 8, 12, 24}\)
  4. \(\color{blue}{1, 2, 4, 5, 8, 10, 20, 40}\)
  5. \(\color{blue}{ 1, 2, 43, 86 }\)
  6. \(\color{blue}{ 1, 2, 3, 6, 13, 26, 39, 78 }\)

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