Greatest Common Factor of 112 and 120

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 112, 120 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 112 and 120 is 8.

GCF(112,120) = 8

GCF of 112 and 120

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

GCF of:
and

Greatest Common Factor of 112 and 120

GCF of 112 and 120 is 8

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

Prime Factorization of 120


2 120
2 60
2 30
3 15
5 5
1

Prime factors of 120 are 2,3,5. Prime factorization of 120 in exponential form is:

120 = 23×31×51

∴ So by taking common prime factors GCF of 112 and 120 is 8

Greatest Common Factor of 112 and 120 by matching factors method

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

Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Greatest Common Factor

We found the factors and prime factorization of 112 and 120. The biggest common factor number is the GCF number.
So the greatest common factor 112 and 120 is 8.

Also check out the Least Common Multiple of 112 and 120

Properties of GCF 112 and 120

(i) The GCF of 112 and 120 is associative

GCF of 112 and 120 = GCF of 120 and 112

Related Greatest Common Factor of 112

Related Greatest Common Factor of 120

Frequently Asked Questions on GCF of 112 and 120

1. What is the GCF of 112 and 120?

Answer: GCF of 112 and 120 is 8.

2. 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.

3. What are the Factors of 120?

Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.

4. How to Find the GCF of 112 and 120?

Answer:

Greatest Common Factor of 112 and 120 = 8

Step 1: Find the prime factorization of 112

112 = 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 120

120 = 2 x 2 x 2 x 3 x 5

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 = 8

Step 4: Therefore, the greatest common factor of 112 and 120 is 8