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 32 and 80 are 1, 2, 4, 8 and 16.
Get Common Factors Of 32 And 80
Here is how you can find the common factors between two numbers in a step-by-step approach.
| Find Common Factors of 32 and 80 |
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| Of the two numbers 32 and 80 start with the smaller number. Which of the two is the smallest? |
| 32 is the smaller of the two numbers. |
| Find all the factors of the smallest number 32. |
| Start by inserting into your factor list both the number 1 and 32. |
| Working factor list contains 1 and 32 |
| Increment the factor by 1: 1 + 1 = 2 |
| Can 2 be divided into 32 without leaving a remainder? |
| Yes! Therefore, add both 2 and the quotient 16 into the factor list. |
| Working factor list contains 1, 2, 16 and 32 |
| Increment the factor by 1: 2 + 1 = 3 |
| Can 3 be divided into 32 without leaving a remainder? |
|
No! 3 divided into
|
| Increment the factor by 1: 3 + 1 = 4 |
| Can 4 be divided into 32 without leaving a remainder? |
| Yes! Therefore, add both 4 and the quotient 8 into the factor list. |
| Working factor list contains 1, 2, 4, 8, 16 and 32 |
| Increment the factor by 1: 4 + 1 = 5 |
| Can 5 be divided into 32 without leaving a remainder? |
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No! 5 divided into
|
| As you have reached (or are about to eclipse) the square root of 32 you can stop here. |
| You now have all the factors of 32 being 1, 2, 4, 8, 16 and 32. |
| 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, 4, 8, 16, 32 ] |
| With the next factor 2 can it be divided into 80 without leaving any remainder? |
| Yes! 80 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 , 4, 8, 16, 32 ] |
| With the next factor 4 can it be divided into 80 without leaving any remainder? |
| Yes! 80 is divisible by 4. |
| Therefore, add this number to your common factor list. |
| Common factors list is now 1, 2 and 4. |
| Progress to the next number in the smaller factor’s list: [ 1 , 2 , 4 , 8, 16, 32 ] |
| With the next factor 8 can it be divided into 80 without leaving any remainder? |
| Yes! 80 is divisible by 8. |
| Therefore, add this number to your common factor list. |
| Common factors list is now 1, 2, 4 and 8. |
| Progress to the next number in the smaller factor’s list: [ 1 , 2 , 4 , 8 , 16, 32 ] |
| With the next factor 16 can it be divided into 80 without leaving any remainder? |
| Yes! 80 is divisible by 16. |
| Therefore, add this number to your common factor list. |
| Common factors list is now 1, 2, 4, 8 and 16. |
| Progress to the next number in the smaller factor’s list: [ 1 , 2 , 4 , 8 , 16 , 32 ] |
| With the next factor 32 can it be divided into 80 without leaving any remainder? |
| No! 80 when divided by 32 has a remainder of 16. |
| Once you’ve finished checking each factor from the smallest number list you will have your common factors of 32 and 80 which are 1, 2, 4, 8 and 16 |
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 32 and 80 are 1, 2, 4, 8 and 16.
You might want to try for yourself and see how you go doing a similar math problem, like finding the common factors of 12 and 18 or maybe the common factors of 18 and 24 .