Factoring Numbers

Factoring Numbers

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

Step by step guide to factoring numbers

  • Factoring numbers means to break 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.

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

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

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

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

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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