Greatest Common Factor

What is Greatest Common Factor?

The largest common factor of two or more numbers is called as Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting a Natural number.

For example – The GCF of 18, 21 is 3.

GCF of 10, 15 and 25 is 5.

Greatest common factor

How to find the GCF?

If we have to find out the GCF of two numbers, we will first list the prime factors of each number. The mutliple of common factors of both the numbers results in GCF. If there are no common prime factors, the greatest common factor is 1.

Finding the GCF of a given number set can be easy. However, there are several steps need to be followed to get the correct GCF. In order to find the greatest common factor of two given numbers, you need to find all the factors of both the numbers and then identify the common factors.

Find out the GCF of 18 and 24

Prime factors of 18\(2 \times 3 \times 3\)

Prime factors of 24\(2 \times 2 \times 2 \times 3\)

They have factors 2 and 3 in common so, thus G.C.F of 18 and 24 is \(2 \times 3\) = 6

GCF and LCM

Greatest Common Factor of two or more numbers is defined as the largest number that is a factor of all the numbers.

Least Common Multiple of two or more numbers is the smallest number (non-zero) that is a multiple of all the numbers.

Factoring Greatest Common Factor:

Factor method is used to list out all the prime factors, and you can easily find out the LCM and GCF. Factors are usually the numbers that we multiply together to get another number.

Example- Factors of 12 – 1,2,3,4,6 and 12 because \(2 \times 6\) =12, \(4 \times 3\) = 12 or \(1 \times 12\) = 12. After finding out the factors of two numbers, we need to circle all the numbers that appear in both the list.

Lets Work Out-

Example- Find the GCF of 18 and 24.

Solution- First list all the factors of the given numbers.

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

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24/

The largest common factor of 18 and 24 is 6.

Thus G.C.F. is 6.

Example- Find the GCF of 8, 18,28 and 48.

Solution- Factors are as follows-

Factors of 8 = 1, 2, 4, 8

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

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

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest common factor of 8, 18, 28, 48 is 2.

Thus G.C.F. is 2.

GCF Online Calculator

Another easy method to calculate the G.C.F of any two or more than two numbers is the calculator. This online GCF calculator will find the G.C.F automatically.


Practise This Question

In the given figure, ABCD is parallelogram.If A=75, then B is