Greatest Common Factor of 2114 and 2120

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 2114, 2120 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2114 and 2120 is 2.

GCF(2114,2120) = 2

GCF of 2114 and 2120

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

GCF of:
and

Greatest Common Factor of 2114 and 2120

GCF of 2114 and 2120 is 2

Prime Factorization of 2114


2 2114
7 1057
151 151
1

Prime factors of 2114 are 2,7,151. Prime factorization of 2114 in exponential form is:

2114 = 21×71×1511

Prime Factorization of 2120


2 2120
2 1060
2 530
5 265
53 53
1

Prime factors of 2120 are 2,5,53. Prime factorization of 2120 in exponential form is:

2120 = 23×51×531

∴ So by taking common prime factors GCF of 2114 and 2120 is 2

Greatest Common Factor of 2114 and 2120 by matching factors method

Factors of 2114

List of positive integer factors of 2114 that divides 2114 without a remainder.

1,2,7,14,151,302,1057,2114

Factors of 2120

List of positive integer factors of 2120 that divides 2120 without a remainder.

1,2,4,5,8,10,20,40,53,106,212,265,424,530,1060,2120

Greatest Common Factor

We found the factors and prime factorization of 2114 and 2120. The biggest common factor number is the GCF number.
So the greatest common factor 2114 and 2120 is 2.

Also check out the Least Common Multiple of 2114 and 2120

Properties of GCF 2114 and 2120

(i) The GCF of 2114 and 2120 is associative

GCF of 2114 and 2120 = GCF of 2120 and 2114

Related Greatest Common Factor of 2114

Related Greatest Common Factor of 2120

Frequently Asked Questions on GCF of 2114 and 2120

1. What is the GCF of 2114 and 2120?

Answer: GCF of 2114 and 2120 is 2.

2. What are the Factors of 2114?

Answer: Factors of 2114 are 1, 2, 7, 14, 151, 302, 1057, 2114. There are 8 integers that are factors of 2114. The greatest factor of 2114 is 2114.

3. What are the Factors of 2120?

Answer: Factors of 2120 are 1, 2, 4, 5, 8, 10, 20, 40, 53, 106, 212, 265, 424, 530, 1060, 2120. There are 16 integers that are factors of 2120. The greatest factor of 2120 is 2120.

4. How to Find the GCF of 2114 and 2120?

Answer:

Greatest Common Factor of 2114 and 2120 = 2

Step 1: Find the prime factorization of 2114

2114 = 2 x 7 x 151

Step 2: Find the prime factorization of 2120

2120 = 2 x 2 x 2 x 5 x 53

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 2114 and 2120 is 2