The largest common factor of two or more numbers is called the highest common factor (HCF).
Greatest common divisor or greatest common factor (GCF)
First find the factors of numbers given, which means;
List all the factors of 12 and 16
Number | Factors |
12 | 1 , 2 , 3 , 4 , 6 , 12 |
16 | 1 , 2 , 4 , 8 , 16 |
Group the common factors.
Common factors are the factors that are found in both lists of factors.
Number | Factors |
12 | 1 , 2 , 3 , 4 , 6 , 12 |
16 | 1 , 2 , 4 , 8 , 16 |
So, the common factors of 12 and 16 are 1 , 2 and 4.
Now choose the highest factor of the common factors.
List all the factors of 15 , 30 and 60
Number | Factors |
15 | 1 , 3 , 5 , 15 |
30 | 1 , 2 , 3, 5, 6 , 10 , 15 , 30 |
60 | 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60 |
Group the common factors.
Number | Factors |
15 | 1 , 3 , 5 , 15 |
30 | 1 , 2 , 3, 5, 6 , 10 , 15 , 30 |
60 | 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60 |
So, common factors of 15 , 30 and 60 are 1 , 3 , 5 and 15.
Hope you have learned the way to find the highest common factor (HCF) or the greatest common factor (greatest common divisor). Try the HCF Quiz.