Greatest Common Factor of 2107 and 2114

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 2107, 2114 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2107 and 2114 is 7.

GCF(2107,2114) = 7

GCF of 2107 and 2114

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

GCF of:
and

Greatest Common Factor of 2107 and 2114

GCF of 2107 and 2114 is 7

Prime Factorization of 2107


7 2107
7 301
43 43
1

Prime factors of 2107 are 7,43. Prime factorization of 2107 in exponential form is:

2107 = 72×431

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

∴ So by taking common prime factors GCF of 2107 and 2114 is 7

Greatest Common Factor of 2107 and 2114 by matching factors method

Factors of 2107

List of positive integer factors of 2107 that divides 2107 without a remainder.

1,7,43,49,301,2107

Factors of 2114

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

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

Greatest Common Factor

We found the factors and prime factorization of 2107 and 2114. The biggest common factor number is the GCF number.
So the greatest common factor 2107 and 2114 is 7.

Also check out the Least Common Multiple of 2107 and 2114

Properties of GCF 2107 and 2114

(i) The GCF of 2107 and 2114 is associative

GCF of 2107 and 2114 = GCF of 2114 and 2107

Related Greatest Common Factor of 2107

Related Greatest Common Factor of 2114

Frequently Asked Questions on GCF of 2107 and 2114

1. What is the GCF of 2107 and 2114?

Answer: GCF of 2107 and 2114 is 7.

2. What are the Factors of 2107?

Answer: Factors of 2107 are 1, 7, 43, 49, 301, 2107. There are 6 integers that are factors of 2107. The greatest factor of 2107 is 2107.

3. 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.

4. How to Find the GCF of 2107 and 2114?

Answer:

Greatest Common Factor of 2107 and 2114 = 7

Step 1: Find the prime factorization of 2107

2107 = 7 x 7 x 43

Step 2: Find the prime factorization of 2114

2114 = 2 x 7 x 151

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

GCF = 7

Step 4: Therefore, the greatest common factor of 2107 and 2114 is 7