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Factors of Numbers
Find GCF of Two Numbers


On this Page:
 1)  Common Factors
 2)  Factor Pairs
 2)  Greatest Common Factor

In Math a factor of a specific number, is another number that divides the specific number exactly.

For example if we look at the number  14.

The numbers  1,  2,  7,  14   are factors of  14.

14 ÷ 1  =  14     ,     14 ÷ 2  =  7     ,     14 ÷ 7  =  2     ,     14 ÷ 14  =  1

So factors of numbers can be multiplied together, to get the given number.

2 × 7  =  14     ,     1 × 14  =  14

Negative numbers can also be considered factors also.         -2 × -7  =  14

So  -1 , -2 , -7 , -14  are also factors of  14.




Factor Pairs

A factor pair of a number, is a set of two factors that multiplied together result in that number.

We can look at the number   42.

The factors of  42  are as follows.     1 , 2 , 3 , 6 , 7 , 14 , 21 , 42

Of these factors,  6  and  7  are a factor pair.     6 × 7  =  42

The factors  3  and  14  are also a factor pair.     3 × 14  =  42

A number can sometimes have more than one factor pair among its factors.




Common Factors

Common factors of numbers, are factors that divide evenly into all of the numbers, and any pair or group of numbers can have more than one common factor.


Examples




1.1

Factors of  8   =>   1 , 2 , 4 , 8

Factors of  20   =>   1 , 2 , 4 , 5 , 10 , 20

1 , 2  and  4  are common factors of  8  and  20.



1.2

Factors of  9   =>   1 , 3 , 9

Factors of  15   =>   1 , 3 , 5 , 15

Factors of  45   =>   1 , 3 , 5 , 9 , 15 , 45

1  and  3  are common factors of  9 , 15  and  12.








Find GCF of Two Numbers
Greatest Common Factor

The greatest common factor (GCF), is simply the largest common factor that a pair of numbers or a group of numbers share in common.

Finding the GCF of two numbers is something that can be helpful when it comes to things such as simplifying fractions.



Examples




2.1

Greatest common factor of  16  and  28?

Solution

To find the greatest common factor, one can list all the factors of each, and find the greatest shared factor.

Factors of  16   =>   1 , 2 , 4 , 8 , 16

Factors of  28   =>   1 , 2 , 4 , 7 , 14 , 28

It can be seen that  4  is the greatest common factor of  28  and  16.



2.2

Greatest common factor of  18  and  42?

Solution

Factors of  18   =>   1 , 2 , 3 , 6 , 9 , 18

Factors of  42   =>   1 , 2 , 3 , 6 , 7 , 14 , 21 , 42

It can be seen that  6  is the greatest common factor of  18  and  42.





There is though another method that can be used to find GCF of two numbers.
Making use of what are known as ‘prime factors’.

Examples of this method can be seen on the  GCF by Prime Factorization  page.




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