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 12 and 18 are 1, 2, 3 and 6.
Get Common Factors Of 12 And 18
Here is how you can find the common factors between two numbers in a step-by-step approach.
| Find Common Factors of 12 and 18 Step By Step |
| Of the two numbers 12 and 18 start with the smaller number. Which of the two is the smallest? |
| 12 is the smaller of the two numbers. |
| Find all the factors of the smallest number 12. |
| Start by inserting into your factor list both the number 1 and 12. |
| Working factor list contains 1 and 12 |
| Increment the factor by 1: 1 + 1 = 2 |
| Can 2 be divided into 12 without leaving a remainder? |
| Yes! Therefore, add both 2 and the quotient 6 into the factor list. |
| Working factor list contains 1, 2, 6 and 12 |
| Increment the factor by 1: 2 + 1 = 3 |
| Can 3 be divided into 12 without leaving a remainder? |
| Yes! Therefore, add both 3 and the quotient 4 into the factor list. |
| Working factor list contains 1, 2, 3, 4, 6 and 12 |
| As you have reached (or are about to eclipse) the square root of 12 you can stop here. |
| You now have all the factors of 12 being 1, 2, 3, 4, 6 and 12. |
| 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, 4, 6, 12 ] |
| With the next factor 2 can it be divided into 18 without leaving any remainder? |
| Yes! 18 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, 4, 6, 12 ] |
| With the next factor 3 can it be divided into 18 without leaving any remainder? |
| Yes! 18 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 , 4, 6, 12 ] |
| With the next factor 4 can it be divided into 18 without leaving any remainder? |
| No! 18 when divided by 4 has a remainder of 2. |
| Progress to the next number in the smaller factor’s list: [ 1 , 2 , 3 , 4 , 6, 12 ] |
| With the next factor 6 can it be divided into 18 without leaving any remainder? |
| Yes! 18 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 , 4 , 6 , 12 ] |
| With the next factor 12 can it be divided into 18 without leaving any remainder? |
| No! 18 when divided by 12 has a remainder of 6. |
| Once you’ve finished checking each factor from the smallest number list you will have your common factors of 12 and 18 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 12 and 18 are 1, 2, 3 and 6.
See how you go trying your hand at finding the common factors of 18 and 24 or perhaps the common factors of 28 and 42 .