How do you find the factors between two numbers? And how can you find them quickly ?
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 28 and 42 are 1, 2, 7 and 14.
Get Common Factors Of 28 And 42
Here is how you can find the common factors between two numbers in a stepbystep approach.
Find Common Factors of 28 and 42 

Of the two numbers 28 and 42 start with the smaller number. Which of the two is the smallest? 
28 is the smaller of the two numbers. 
Find all the factors of the smallest number 28. 
Start by inserting into your factor list both the number 1 and 28. 
Working factor list contains 1 and 28 
Increment the factor by 1: 1 + 1 = 2 
Can 2 be divided into 28 without leaving a remainder? 
Yes! Therefore, add both 2 and the quotient 14 into the factor list. 
Working factor list contains 1, 2, 14 and 28 
Increment the factor by 1: 2 + 1 = 3 
Can 3 be divided into 28 without leaving a remainder? 
No! 3 divided into

Increment the factor by 1: 3 + 1 = 4 
Can 4 be divided into 28 without leaving a remainder? 
Yes! Therefore, add both 4 and the quotient 7 into the factor list. 
Working factor list contains 1, 2, 4, 7, 14 and 28 
Increment the factor by 1: 4 + 1 = 5 
Can 5 be divided into 28 without leaving a remainder? 
No! 5 divided into

As you have reached (or are about to eclipse) the square root of 28 you can stop here. 
You now have all the factors of 28 being 1, 2, 4, 7, 14 and 28. 
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, 7, 14, 28 ] 
With the next factor 2 can it be divided into 42 without leaving any remainder? 
Yes! 42 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, 7, 14, 28 ] 
With the next factor 4 can it be divided into 42 without leaving any remainder? 
No! 42 when divided by 4 has a remainder of 2. 
Progress to the next number in the smaller factor’s list: [ 1 , 2 , 4 , 7, 14, 28 ] 
With the next factor 7 can it be divided into 42 without leaving any remainder? 
Yes! 42 is divisible by 7. 
Therefore, add this number to your common factor list. 
Common factors list is now 1, 2 and 7. 
Progress to the next number in the smaller factor’s list: [ 1 , 2 , 4 , 7 , 14, 28 ] 
With the next factor 14 can it be divided into 42 without leaving any remainder? 
Yes! 42 is divisible by 14. 
Therefore, add this number to your common factor list. 
Common factors list is now 1, 2, 7 and 14. 
Progress to the next number in the smaller factor’s list: [ 1 , 2 , 4 , 7 , 14 , 28 ] 
With the next factor 28 can it be divided into 42 without leaving any remainder? 
No! 42 when divided by 28 has a remainder of 14. 
Once you’ve finished checking each factor from the smallest number list you will have your common factors of 28 and 42 which are 1, 2, 7 and 14 
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 28 and 42 are 1, 2, 7 and 14.
Next, you might want to try and see how you go finding the common factors of 12 and 18 , or the common factors of 32 and 80 .