# 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

1. Factoring numbers means to break the numbers into their prime factors.
2. First few prime numbers: $$2, 3, 5, 7, 11, 13, 17, 19$$
3. 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.

• $$\color{blue}{68}$$
• $$\color{blue}{56}$$
• $$\color{blue}{24}$$
• $$\color{blue}{40}$$
• $$\color{blue}{86}$$
• $$\color{blue}{78}$$

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