Greatest Common Factor of 105 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 105, 108 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 105 and 108 is 3.

GCF(105,108) = 3

GCF of 105 and 108

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

GCF of:
and

Greatest Common Factor of 105 and 108

GCF of 105 and 108 is 3

Prime Factorization of 105


3 105
5 35
7 7
1

Prime factors of 105 are 3,5,7. Prime factorization of 105 in exponential form is:

105 = 31×51×71

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 105 and 108 is 3

Greatest Common Factor of 105 and 108 by matching factors method

Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1,3,5,7,15,21,35,105

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 105 and 108. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 108 is 3.

Also check out the Least Common Multiple of 105 and 108

Properties of GCF 105 and 108

(i) The GCF of 105 and 108 is associative

GCF of 105 and 108 = GCF of 108 and 105

Related Greatest Common Factor of 105

Related Greatest Common Factor of 108

Frequently Asked Questions on GCF of 105 and 108

1. What is the GCF of 105 and 108?

Answer: GCF of 105 and 108 is 3.

2. What are the Factors of 105?

Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.

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 105 and 108?

Answer:

Greatest Common Factor of 105 and 108 = 3

Step 1: Find the prime factorization of 105

105 = 3 x 5 x 7

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 = 3

Step 4: Therefore, the greatest common factor of 105 and 108 is 3