Greatest Common Factor of 112 and 116

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, 116 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 112 and 116 is 4.

GCF(112,116) = 4

GCF of 112 and 116

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

GCF of:
and

Greatest Common Factor of 112 and 116

GCF of 112 and 116 is 4

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 116


2 116
2 58
29 29
1

Prime factors of 116 are 2,29. Prime factorization of 116 in exponential form is:

116 = 22×291

∴ So by taking common prime factors GCF of 112 and 116 is 4

Greatest Common Factor of 112 and 116 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 116

List of positive integer factors of 116 that divides 116 without a remainder.

1,2,4,29,58,116

Greatest Common Factor

We found the factors and prime factorization of 112 and 116. The biggest common factor number is the GCF number.
So the greatest common factor 112 and 116 is 4.

Also check out the Least Common Multiple of 112 and 116

Properties of GCF 112 and 116

(i) The GCF of 112 and 116 is associative

GCF of 112 and 116 = GCF of 116 and 112

Related Greatest Common Factor of 112

Related Greatest Common Factor of 116

Frequently Asked Questions on GCF of 112 and 116

1. What is the GCF of 112 and 116?

Answer: GCF of 112 and 116 is 4.

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 116?

Answer: Factors of 116 are 1, 2, 4, 29, 58, 116. There are 6 integers that are factors of 116. The greatest factor of 116 is 116.

4. How to Find the GCF of 112 and 116?

Answer:

Greatest Common Factor of 112 and 116 = 4

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 116

116 = 2 x 2 x 29

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 112 and 116 is 4