Greatest Common Factor of 100 and 108

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 100, 108 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 100 and 108 is 4.

GCF(100,108) = 4

GCF of 100 and 108

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 100 and 108

GCF of 100 and 108 is 4

Prime Factorization of 100


2 100
2 50
5 25
5 5
1

Prime factors of 100 are 2,5. Prime factorization of 100 in exponential form is:

100 = 22×52

Prime Factorization of 108


2 108
2 54
3 27
3 9
3 3
1

Prime factors of 108 are 2,3. Prime factorization of 108 in exponential form is:

108 = 22×33

∴ So by taking common prime factors GCF of 100 and 108 is 4

Greatest Common Factor of 100 and 108 by matching factors method

Factors of 100

List of positive integer factors of 100 that divides 100 without a remainder.

1,2,4,5,10,20,25,50,100

Factors of 108

List of positive integer factors of 108 that divides 108 without a remainder.

1,2,3,4,6,9,12,18,27,36,54,108

Greatest Common Factor

We found the factors and prime factorization of 100 and 108. The biggest common factor number is the GCF number.
So the greatest common factor 100 and 108 is 4.

Also check out the Least Common Multiple of 100 and 108

Properties of GCF 100 and 108

(i) The GCF of 100 and 108 is associative

GCF of 100 and 108 = GCF of 108 and 100

Related Greatest Common Factor of 100

Related Greatest Common Factor of 108

Frequently Asked Questions on GCF of 100 and 108

1. What is the GCF of 100 and 108?

Answer: GCF of 100 and 108 is 4.

2. What are the Factors of 100?

Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.

3. What are the Factors of 108?

Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.

4. How to Find the GCF of 100 and 108?

Answer:

Greatest Common Factor of 100 and 108 = 4

Step 1: Find the prime factorization of 100

100 = 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 108

108 = 2 x 2 x 3 x 3 x 3

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 100 and 108 is 4