Greatest Common Factor of 2014 and 2016

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, 2016 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2014 and 2016 is 2.

GCF(2014,2016) = 2

GCF of 2014 and 2016

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

GCF of:
and

Greatest Common Factor of 2014 and 2016

GCF of 2014 and 2016 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 2016


2 2016
2 1008
2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 2016 are 2,3,7. Prime factorization of 2016 in exponential form is:

2016 = 25×32×71

∴ So by taking common prime factors GCF of 2014 and 2016 is 2

Greatest Common Factor of 2014 and 2016 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 2016

List of positive integer factors of 2016 that divides 2016 without a remainder.

1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,32,36,42,48,56,63,72,84,96,112,126,144,168,224,252,288,336,504,672,1008,2016

Greatest Common Factor

We found the factors and prime factorization of 2014 and 2016. The biggest common factor number is the GCF number.
So the greatest common factor 2014 and 2016 is 2.

Also check out the Least Common Multiple of 2014 and 2016

Properties of GCF 2014 and 2016

(i) The GCF of 2014 and 2016 is associative

GCF of 2014 and 2016 = GCF of 2016 and 2014

Related Greatest Common Factor of 2014

Related Greatest Common Factor of 2016

Frequently Asked Questions on GCF of 2014 and 2016

1. What is the GCF of 2014 and 2016?

Answer: GCF of 2014 and 2016 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 2016?

Answer: Factors of 2016 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016. There are 36 integers that are factors of 2016. The greatest factor of 2016 is 2016.

4. How to Find the GCF of 2014 and 2016?

Answer:

Greatest Common Factor of 2014 and 2016 = 2

Step 1: Find the prime factorization of 2014

2014 = 2 x 19 x 53

Step 2: Find the prime factorization of 2016

2016 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7

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 2016 is 2