Greatest Common Factor of 2014 and 2022

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 2014, 2022 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2014 and 2022 is 2.

GCF(2014,2022) = 2

GCF of 2014 and 2022

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

GCF of:
and

Greatest Common Factor of 2014 and 2022

GCF of 2014 and 2022 is 2

Prime Factorization of 2014


2 2014
19 1007
53 53
1

Prime factors of 2014 are 2,19,53. Prime factorization of 2014 in exponential form is:

2014 = 21×191×531

Prime Factorization of 2022


2 2022
3 1011
337 337
1

Prime factors of 2022 are 2,3,337. Prime factorization of 2022 in exponential form is:

2022 = 21×31×3371

∴ So by taking common prime factors GCF of 2014 and 2022 is 2

Greatest Common Factor of 2014 and 2022 by matching factors method

Factors of 2014

List of positive integer factors of 2014 that divides 2014 without a remainder.

1,2,19,38,53,106,1007,2014

Factors of 2022

List of positive integer factors of 2022 that divides 2022 without a remainder.

1,2,3,6,337,674,1011,2022

Greatest Common Factor

We found the factors and prime factorization of 2014 and 2022. The biggest common factor number is the GCF number.
So the greatest common factor 2014 and 2022 is 2.

Also check out the Least Common Multiple of 2014 and 2022

Properties of GCF 2014 and 2022

(i) The GCF of 2014 and 2022 is associative

GCF of 2014 and 2022 = GCF of 2022 and 2014

Related Greatest Common Factor of 2014

Related Greatest Common Factor of 2022

Frequently Asked Questions on GCF of 2014 and 2022

1. What is the GCF of 2014 and 2022?

Answer: GCF of 2014 and 2022 is 2.

2. What are the Factors of 2014?

Answer: Factors of 2014 are 1, 2, 19, 38, 53, 106, 1007, 2014. There are 8 integers that are factors of 2014. The greatest factor of 2014 is 2014.

3. What are the Factors of 2022?

Answer: Factors of 2022 are 1, 2, 3, 6, 337, 674, 1011, 2022. There are 8 integers that are factors of 2022. The greatest factor of 2022 is 2022.

4. How to Find the GCF of 2014 and 2022?

Answer:

Greatest Common Factor of 2014 and 2022 = 2

Step 1: Find the prime factorization of 2014

2014 = 2 x 19 x 53

Step 2: Find the prime factorization of 2022

2022 = 2 x 3 x 337

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 2014 and 2022 is 2