Greatest Common Factor of 109 and 114

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 109, 114 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 109 and 114 is 1.

GCF(109,114) = 1

GCF of 109 and 114

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

GCF of:
and

Greatest Common Factor of 109 and 114

GCF of 109 and 114 is 1

Prime Factorization of 109


109 109
1

Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:

109 = 1091

Prime Factorization of 114


2 114
3 57
19 19
1

Prime factors of 114 are 2.Prime factorization of 114 in exponential form is:

114 = 21×31×191

∴ So by taking common prime factors GCF of 109 and 114 is 1

Greatest Common Factor of 109 and 114 by matching factors method

Factors of 109

List of positive integer factors of 109 that divides 109 without a remainder.

1,109

Factors of 114

List of positive integer factors of 114 that divides 114 without a remainder.

1,2,3,6,19,38,57,114

Greatest Common Factor

We found the factors and prime factorization of 109 and 114. The biggest common factor number is the GCF number.
So the greatest common factor 109 and 114 is 1.

Also check out the Least Common Multiple of 109 and 114

Properties of GCF 109 and 114

(i) The GCF of 109 and 114 is associative

GCF of 109 and 114 = GCF of 114 and 109

Related Greatest Common Factor of 109

Related Greatest Common Factor of 114

Frequently Asked Questions on GCF of 109 and 114

1. What is the GCF of 109 and 114?

Answer: GCF of 109 and 114 is 1.

2. What are the Factors of 109?

Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.

3. What are the Factors of 114?

Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.

4. How to Find the GCF of 109 and 114?

Answer:

Greatest Common Factor of 109 and 114 = 1

Step 1: Find the prime factorization of 109

109 = 109

Step 2: Find the prime factorization of 114

114 = 2 x 3 x 19

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 109 and 114 is 1