Greatest Common Factor of 106 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 106, 112 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 106 and 112 is 2.

GCF(106,112) = 2

GCF of 106 and 112

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

GCF of:
and

Greatest Common Factor of 106 and 112

GCF of 106 and 112 is 2

Prime Factorization of 106


2 106
53 53
1

Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:

106 = 21×531

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 106 and 112 is 2

Greatest Common Factor of 106 and 112 by matching factors method

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1,2,53,106

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 106 and 112. The biggest common factor number is the GCF number.
So the greatest common factor 106 and 112 is 2.

Also check out the Least Common Multiple of 106 and 112

Properties of GCF 106 and 112

(i) The GCF of 106 and 112 is associative

GCF of 106 and 112 = GCF of 112 and 106

Related Greatest Common Factor of 106

Related Greatest Common Factor of 112

Frequently Asked Questions on GCF of 106 and 112

1. What is the GCF of 106 and 112?

Answer: GCF of 106 and 112 is 2.

2. What are the Factors of 106?

Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.

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 106 and 112?

Answer:

Greatest Common Factor of 106 and 112 = 2

Step 1: Find the prime factorization of 106

106 = 2 x 53

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

Step 4: Therefore, the greatest common factor of 106 and 112 is 2