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