What is Greatest Common Factor or GCF?
The greatest common factor (gcf) of two or more given numbers is the greatest factor that exactly divides the given numbers. It is called gcf in short.
How to find the greatest common factor?
To find the gcf of two or more numbers following steps are used:
Method 1:
Find all the factors of the given numbers and then find
the common factor which is the greatest.
For example: Find the gcf of 18 and 30. We will write all the
factors of 18 and 30 as shown below:
Method 1:
Find all the factors of the given numbers and then find
the common factor which is the greatest.
For example: Find the gcf of 18 and 30. We will write all the
factors of 18 and 30 as shown below:
- 18 = 1, 2, 3, 6, 9, 18
- 30 = 1, 2, 3, 5, 6, 10, 15, 30
The common factors are 1, 2, 3 and 6. Now we have to pick
the greatest common factor which is 6 obviously.
Hence gcf of 18 and 30 is 6.
Method 2:
- Find all the prime factors of each number.
- Multiply the common factors from the above list to find the gcf.
For example; Let's find the gcf of 12 and 18:
- Find the prime factors of 12 and 18 as follows:
- 12 = 2 x 2 x 3
- 18 = 2 x 3 x 3
- Now the common factors are 2 and 3 (Colored in red). Multiply them as shown below to get the gcf of 12 and 18:
gcf of 12 and 18 = 2 x 3 = 6 answer
Remember if there is no common factor found then the gcf is 1.
Now do the following worksheets to practice the concept of the gcf:
Finding gcf using all the factors of two or more numbers given:
