Greatest Common Factor of 106 and 110

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, 110 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 106 and 110 is 2.

GCF(106,110) = 2

GCF of 106 and 110

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

GCF of:
and

Greatest Common Factor of 106 and 110

GCF of 106 and 110 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 110


2 110
5 55
11 11
1

Prime factors of 110 are 2,5,11. Prime factorization of 110 in exponential form is:

110 = 21×51×111

∴ So by taking common prime factors GCF of 106 and 110 is 2

Greatest Common Factor of 106 and 110 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 110

List of positive integer factors of 110 that divides 110 without a remainder.

1,2,5,10,11,22,55,110

Greatest Common Factor

We found the factors and prime factorization of 106 and 110. The biggest common factor number is the GCF number.
So the greatest common factor 106 and 110 is 2.

Also check out the Least Common Multiple of 106 and 110

Properties of GCF 106 and 110

(i) The GCF of 106 and 110 is associative

GCF of 106 and 110 = GCF of 110 and 106

Related Greatest Common Factor of 106

Related Greatest Common Factor of 110

Frequently Asked Questions on GCF of 106 and 110

1. What is the GCF of 106 and 110?

Answer: GCF of 106 and 110 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 110?

Answer: Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. There are 8 integers that are factors of 110. The greatest factor of 110 is 110.

4. How to Find the GCF of 106 and 110?

Answer:

Greatest Common Factor of 106 and 110 = 2

Step 1: Find the prime factorization of 106

106 = 2 x 53

Step 2: Find the prime factorization of 110

110 = 2 x 5 x 11

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 110 is 2