Greatest Common Factor of 2014 and 2020

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, 2020 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2014 and 2020 is 2.

GCF(2014,2020) = 2

GCF of 2014 and 2020

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

GCF of:
and

Greatest Common Factor of 2014 and 2020

GCF of 2014 and 2020 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 2020


2 2020
2 1010
5 505
101 101
1

Prime factors of 2020 are 2,5,101. Prime factorization of 2020 in exponential form is:

2020 = 22×51×1011

∴ So by taking common prime factors GCF of 2014 and 2020 is 2

Greatest Common Factor of 2014 and 2020 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 2020

List of positive integer factors of 2020 that divides 2020 without a remainder.

1,2,4,5,10,20,101,202,404,505,1010,2020

Greatest Common Factor

We found the factors and prime factorization of 2014 and 2020. The biggest common factor number is the GCF number.
So the greatest common factor 2014 and 2020 is 2.

Also check out the Least Common Multiple of 2014 and 2020

Properties of GCF 2014 and 2020

(i) The GCF of 2014 and 2020 is associative

GCF of 2014 and 2020 = GCF of 2020 and 2014

Related Greatest Common Factor of 2014

Related Greatest Common Factor of 2020

Frequently Asked Questions on GCF of 2014 and 2020

1. What is the GCF of 2014 and 2020?

Answer: GCF of 2014 and 2020 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 2020?

Answer: Factors of 2020 are 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020. There are 12 integers that are factors of 2020. The greatest factor of 2020 is 2020.

4. How to Find the GCF of 2014 and 2020?

Answer:

Greatest Common Factor of 2014 and 2020 = 2

Step 1: Find the prime factorization of 2014

2014 = 2 x 19 x 53

Step 2: Find the prime factorization of 2020

2020 = 2 x 2 x 5 x 101

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 2020 is 2