How do you find the factors between two numbers?

To find the factors between two numbers simply compare the factors of each numbers and whichever number is a factor for both is known as a
*
common factor
*
.

For example, the common factors for the numbers 18 and 24 are 1, 2, 3 and 6.

## Get Common Factors Of 18 And 24

Here is how you can find the common factors between two numbers in a step-by-step approach.

Find Common Factors of 18 and 24 |
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Of the two numbers 18 and 24 start with the smaller number. Which of the two is the smallest? |

18 is the smaller of the two numbers. |

Find all the factors of the smallest number 18. |

Start by inserting into your factor list both the number 1 and 18. |

Working factor list contains 1 and 18 |

Increment the factor by 1: 1 + 1 = 2 |

Can 2 be divided into 18 without leaving a remainder? |

Yes! Therefore, add both 2 and the quotient 9 into the factor list. |

Working factor list contains 1, 2, 9 and 18 |

Increment the factor by 1: 2 + 1 = 3 |

Can 3 be divided into 18 without leaving a remainder? |

Yes! Therefore, add both 3 and the quotient 6 into the factor list. |

Working factor list contains 1, 2, 3, 6, 9 and 18 |

Increment the factor by 1: 3 + 1 = 4 |

Can 4 be divided into 18 without leaving a remainder? |

No! 4 divided into leaves a remainder of 2. |

As you have reached (or are about to eclipse) the square root of 18 you can stop here. |

You now have all the factors of 18 being 1, 2, 3, 6, 9 and 18. |

For each of the factors of the smallest number check each number to see if it divisible by the bigger number. |

As the number 1 is a factor for every integer you can add this automatically to your common factor list. |

Common factor list contains just 1! |

Progress to the next number in the smaller factor’s list: [ 1 , 2, 3, 6, 9, 18 ] |

With the next factor 2 can it be divided into 24 without leaving any remainder? |

Yes! 24 is divisible by 2. |

Therefore, add this number to your common factor list. |

Common factors list is now 1 and 2. |

Progress to the next number in the smaller factor’s list: [ 1 , 2 , 3, 6, 9, 18 ] |

With the next factor 3 can it be divided into 24 without leaving any remainder? |

Yes! 24 is divisible by 3. |

Therefore, add this number to your common factor list. |

Common factors list is now 1, 2 and 3. |

Progress to the next number in the smaller factor’s list: [ 1 , 2 , 3 , 6, 9, 18 ] |

With the next factor 6 can it be divided into 24 without leaving any remainder? |

Yes! 24 is divisible by 6. |

Therefore, add this number to your common factor list. |

Common factors list is now 1, 2, 3 and 6. |

Progress to the next number in the smaller factor’s list: [ 1 , 2 , 3 , 6 , 9, 18 ] |

With the next factor 9 can it be divided into 24 without leaving any remainder? |

No! 24 when divided by 9 has a remainder of 6. |

Progress to the next number in the smaller factor’s list: [ 1 , 2 , 3 , 6 , 9 , 18 ] |

With the next factor 18 can it be divided into 24 without leaving any remainder? |

No! 24 when divided by 18 has a remainder of 6. |

Once you’ve finished checking each factor from the smallest number list you will have your common factors of 18 and 24 which are 1, 2, 3 and 6 |

## Summary

Finding the factors of two different numbers is done by finding the factors of both and where factors from each are the same they are
*
common
*
to both.

The quickest way to find the common factors between two numbers is to find all the factors of the smallest of the two numbers and then from that list see if each number can be divided into the bigger number without leaving a remainder.

The list of numbers that are both factors of the smaller number
**
and
**
can be divided into the bigger number without remainder are your
*
common factors
*
.

The common factors of 18 and 24 are 1, 2, 3 and 6.