Greatest Common Factor of 2010 and 2014

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 2010, 2014 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2010 and 2014 is 2.

GCF(2010,2014) = 2

GCF of 2010 and 2014

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

GCF of:
and

Greatest Common Factor of 2010 and 2014

GCF of 2010 and 2014 is 2

Prime Factorization of 2010


2 2010
3 1005
5 335
67 67
1

Prime factors of 2010 are 2,3,5,67. Prime factorization of 2010 in exponential form is:

2010 = 21×31×51×671

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

∴ So by taking common prime factors GCF of 2010 and 2014 is 2

Greatest Common Factor of 2010 and 2014 by matching factors method

Factors of 2010

List of positive integer factors of 2010 that divides 2010 without a remainder.

1,2,3,5,6,10,15,30,67,134,201,335,402,670,1005,2010

Factors of 2014

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

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

Greatest Common Factor

We found the factors and prime factorization of 2010 and 2014. The biggest common factor number is the GCF number.
So the greatest common factor 2010 and 2014 is 2.

Also check out the Least Common Multiple of 2010 and 2014

Properties of GCF 2010 and 2014

(i) The GCF of 2010 and 2014 is associative

GCF of 2010 and 2014 = GCF of 2014 and 2010

Related Greatest Common Factor of 2010

Related Greatest Common Factor of 2014

Frequently Asked Questions on GCF of 2010 and 2014

1. What is the GCF of 2010 and 2014?

Answer: GCF of 2010 and 2014 is 2.

2. What are the Factors of 2010?

Answer: Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010. There are 16 integers that are factors of 2010. The greatest factor of 2010 is 2010.

3. 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.

4. How to Find the GCF of 2010 and 2014?

Answer:

Greatest Common Factor of 2010 and 2014 = 2

Step 1: Find the prime factorization of 2010

2010 = 2 x 3 x 5 x 67

Step 2: Find the prime factorization of 2014

2014 = 2 x 19 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 2010 and 2014 is 2