Once you learn how to find the prime factors of 28 you can use these skills to find the prime factors of other numbers.

As a high school mathematics teacher for over 14 years I have seen first hand that the students who have mastered the skill of factoring are able to apply this to fractions, algebra and more topics with ease. Freeing up their working memory in their brain for harder concepts.

So read on to learn how to find the prime factors of 28.

## What are the factors of 28?

The factors of 28 are the whole numbers that 28 can be divided by without any remainder.

They are 1, 2, 4, 7, 14 & 28.

## What is the prime factorization of 28?

The prime factorization of 28 is 2 x 2 x 7.

To find the prime factorization of 28 I like to draw a factor tree until I end up with 2 prime numbers at the end of the branch.

Prime numbers have exactly 2 factors, 1 and itself.

Here is a factor tree for 28:

## Video Tutorial on Finding the Prime Factors of 28

## How to find the prime factors of 28

Here are 3 methods to find the factors of 28:

- Using the divisibility rules
- Using a calculator
- Drawing a factor rainbow

### Using the Divisibility rules

Divisor | Rule | Is the divisor a factor of 28? |

1 | Every number is divisible by 1 | yes |

2 | Ends is 2,4,6,8 or 0 | 28 ends in 8, so yes 2 is a factor of 28. |

3 | Sum of digits is divisible by 3 | 2+8=10 which is not divisible by 3, so 3 is not a factor of 28. |

4 | Last 2 digits is divisible by 4 | 4 x 7 = 28, so 4 is a factor of 28. |

5 | Ends in 5 or 0 | 28 ends in 8, not 5 or 0, so 5 is not a factor of 28. |

6 | Divisible by 2 & 3 | Not divisible by both 2 & 3 so 6 is not a factor of 28. |

7 | No test | 7 x 4 = 28, so 7 is a factor of 28. |

8 | Halve it then use the test for 4 | Half of 28 is 14, 14 is not divisible by 4, so 8 is not a factors of 28. |

9 | Sum of digits is divisible by 9 | 2+8 = 10 which is not divisible by 9, so 9 is not a factor of 28. |

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

You can use these divisibility rules to find the factors of 28. Once you have found the factors of 28 you can identify which factors are prime numbers. Then you have found the prime factors of 28.

### Using a calculator

I like to use a simple scientific calculator like this Casio.

To find the prime factors of 28 using a calculator you simply start with 28 then divide by every whole number between 1 and 28. If the answer is a whole number then both the number you are dividing by (the divisor) and the answer (the quotient) are factors of 28.

For example, enter 28 ÷ 2 into your calculator.

Since 28 ÷ 2 = 14, both 2 and 14 are factors of 28.

Then try 28 ÷ 3 on your calculator.

Since the answer is not a whole number, 3 is not a factor of 28.

You don’t really need to keep testing every whole number between 1 and 28.

Once you have found that 28 ÷ 2 = 14, you only need to test the whole numbers up to 14.

Once you have found the factors of 28, you need to identify which of these factors are prime numbers and then you have found the prime factors of 28.

### Drawing a factor rainbow for 28

Start with 1 and 28, then move onto the next whole number after 1 which is 2.

Draw another colour arc for 2 and 14.

Test the next whole number after 2 which is 3. It isn’t a factor so then test 4.

4 is a factor of 28 so draw another arc for 4 and 7.

There are no more whole numbers between 4 & 7 that are factors of 28.

Here is a factor rainbow for 28.

Once you have drawn a factor rainbow you can circle the prime numbers.

I have circled the prime factors of 28, showing 2 and 7.

## What are the factors pairs of 28?

I like to draw a factor rainbow to find all the factor pairs for any number.

The factor pairs can be wrriten as a product like this:

1 x 28 = 28

2 x 14 = 28

4 x 7 = 28

## What is the product of prime factors of 28?

The product of prime factors of 28 is 28 = 2 x 2 x 7.

## Negative factors of 28

The negative factors of 28 are -1, -2, -4, -7, -14 & -28.

Both factors must be negative so that when multiplied together the answer is positive 28.

## FAQs

### What is the factor tree of 28?

28

/ \

2 14

/ \

2 7

### What are the multiples of 28?

The first 10 multiples of 28 are 28, 56, 84, 112, 140, 168, 196, 224, 252, 280.

## Conclusion

Now that you know all about the factors of 28, it’s time to put your knowledge into practice!

Look for opportunities to find factor pairs in your everyday life – at the store, at school, even when you’re out for a walk.

The more you practice, the easier it will become. And before you know it, you’ll be a math pro!

## Further factors

Learn more about the factors of other numbers here.