Greatest Common Factor of 96 and 112

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, 112 i.e. 16 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 96 and 112 is 16.

GCF(96,112) = 16

GCF of 96 and 112

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

GCF of:
and

Greatest Common Factor of 96 and 112

GCF of 96 and 112 is 16

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 112


2 112
2 56
2 28
2 14
7 7
1

Prime factors of 112 are 2,7. Prime factorization of 112 in exponential form is:

112 = 24×71

∴ So by taking common prime factors GCF of 96 and 112 is 16

Greatest Common Factor of 96 and 112 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 112

List of positive integer factors of 112 that divides 112 without a remainder.

1,2,4,7,8,14,16,28,56,112

Greatest Common Factor

We found the factors and prime factorization of 96 and 112. The biggest common factor number is the GCF number.
So the greatest common factor 96 and 112 is 16.

Also check out the Least Common Multiple of 96 and 112

Properties of GCF 96 and 112

(i) The GCF of 96 and 112 is associative

GCF of 96 and 112 = GCF of 112 and 96

Related Greatest Common Factor of 96

Related Greatest Common Factor of 112

Frequently Asked Questions on GCF of 96 and 112

1. What is the GCF of 96 and 112?

Answer: GCF of 96 and 112 is 16.

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 112?

Answer: Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 integers that are factors of 112. The greatest factor of 112 is 112.

4. How to Find the GCF of 96 and 112?

Answer:

Greatest Common Factor of 96 and 112 = 16

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 112

112 = 2 x 2 x 2 x 2 x 7

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

GCF = 2 x 2 x 2 x 2 = 16

Step 4: Therefore, the greatest common factor of 96 and 112 is 16