Let’s find the prime factors of 8 by first finding the factors of 8.

## What are the factors of 8?

The factors of 8 are 1, 2, 4 & 8.

These are numbers that 8 can be divided by exactly with no remainder.

Out of these factors, the only number that is a prime number is 2.

So the only prime factor of 8 is 2.

## What is the prime factorization of 8?

The prime factorization for 8 can be found by drawing a factor tree.

The prime numbers are circled in red.

Prime numbers have exactly 2 factors, 1 and itself. So 2 is a prime factor of 8.

The prime factorization of 8 is 2 x 2 x 2

## How to find the prime factors of 8

There are 3 ways to find the factors of 8.

- divisibility rules
- calculator
- factor rainbow

### Using the Divisibility rules for 8

Divisor | Rule | Is the divisor a factor of 8? |

1 | Every number is divisible by 1 | yes |

2 | Ends is 2,4,6,8 or 0 | 8 ends in 8, so yes 2 is a factor of 8. |

3 | Sum of digits is divisible by 3 | 8 is not divisible by 3, so 3 is not a factor of 8. |

4 | Last 2 digits is divisible by 4 | 4 x 2 = 8, so 4 is a factor of 8. |

5 | Ends in 5 or 0 | 8 ends in 8, not 5 or 0, so 5 is not a factor of 8. |

6 | Divisible by 2 & 3 | Not divisible by both 2 & 3 so 6 is not a factor of 8. |

7 | No test | 7 is not a factor of 8. |

8 | Halve it then use the test for 4 | 1 x 8 = 8, so 8 is a factor of 8. |

9 | Sum of digits is divisible by 9 | 8 is not divisible by 9, so 9 is not a factor of 8. |

10 | Ends in 0 | 28 does not end in 0 so 10 is not a factor of 8. |

### Using a calculator to find the factors of 8

A simple scientific calculator like this Casio can be used to find the factors of 8.

Step 1: Type in 8 ÷ 1. Since this equals a whole number, 8, then 1 is a factor of 8.

Step 2: Type in 8 ÷2. This equals 4 which is a whole number, so both 2 and 4 are factors of 8.

Step 3: Type in 8 ÷ 3. Since this does not equal a whole number, 3 is not a factor of 8.

Of these factors (1, 2 & 4), only 2 is a prime number, so the only prime factor of 8 is 2.

### Drawing a factor a rainbow for 8

A factor rainbow is a nice colourful method for visual learners to see pairs of numbers (factors) that multiply together to equal 8.

Here is a factor rainbow for 8

## What are the factors pairs of 8?

Factor pairs can be found be drawing a factor rainbow.

1 x 8 = 8

and 2 x 4 = 8

There are no more whole numbers between 2 and 4 that are factors of 8.

So the factor pairs of 8 are (1,8) and (2,4).

## What is the product of prime factors of 8?

The prime factorization of 8 is 2 x 2 x 2.

So we can express 8 as a product of prime factors like this:

8 = 2 x 2 x 2

We can write this in index notation like this:

## Negative factors of 8

The negative factors of 8 are -1,-2,-4 & -8.

Both factors need to be negative so that when multiplied the answer is positive 8.

## FAQs

What is the sum of the factors of 8?

1+2+4+8= 15 so the sum of the factors of 8 is 15.

## Conclusion

## Further factors

Learn more about the factors of other numbers here.