Greatest Common Factor of 96 and 105

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 96, 105 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 96 and 105 is 3.

GCF(96,105) = 3

GCF of 96 and 105

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

GCF of:
and

Greatest Common Factor of 96 and 105

GCF of 96 and 105 is 3

Prime Factorization of 96


2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 96 are 2,3. Prime factorization of 96 in exponential form is:

96 = 25×31

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

∴ So by taking common prime factors GCF of 96 and 105 is 3

Greatest Common Factor of 96 and 105 by matching factors method

Factors of 96

List of positive integer factors of 96 that divides 96 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,96

Factors of 105

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

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

Greatest Common Factor

We found the factors and prime factorization of 96 and 105. The biggest common factor number is the GCF number.
So the greatest common factor 96 and 105 is 3.

Also check out the Least Common Multiple of 96 and 105

Properties of GCF 96 and 105

(i) The GCF of 96 and 105 is associative

GCF of 96 and 105 = GCF of 105 and 96

Related Greatest Common Factor of 96

Related Greatest Common Factor of 105

Frequently Asked Questions on GCF of 96 and 105

1. What is the GCF of 96 and 105?

Answer: GCF of 96 and 105 is 3.

2. What are the Factors of 96?

Answer: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. There are 12 integers that are factors of 96. The greatest factor of 96 is 96.

3. 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.

4. How to Find the GCF of 96 and 105?

Answer:

Greatest Common Factor of 96 and 105 = 3

Step 1: Find the prime factorization of 96

96 = 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 105

105 = 3 x 5 x 7

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 96 and 105 is 3