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.

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

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. $$\color{blue}{ 1, 2, 3, 6, 13, 26, 39, 78 }$$