Greatest Common Factor of 2004 and 2012

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 2004, 2012 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2004 and 2012 is 4.

GCF(2004,2012) = 4

GCF of 2004 and 2012

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

GCF of:
and

Greatest Common Factor of 2004 and 2012

GCF of 2004 and 2012 is 4

Prime Factorization of 2004


2 2004
2 1002
3 501
167 167
1

Prime factors of 2004 are 2,3,167. Prime factorization of 2004 in exponential form is:

2004 = 22×31×1671

Prime Factorization of 2012


2 2012
2 1006
503 503
1

Prime factors of 2012 are 2,503. Prime factorization of 2012 in exponential form is:

2012 = 22×5031

∴ So by taking common prime factors GCF of 2004 and 2012 is 4

Greatest Common Factor of 2004 and 2012 by matching factors method

Factors of 2004

List of positive integer factors of 2004 that divides 2004 without a remainder.

1,2,3,4,6,12,167,334,501,668,1002,2004

Factors of 2012

List of positive integer factors of 2012 that divides 2012 without a remainder.

1,2,4,503,1006,2012

Greatest Common Factor

We found the factors and prime factorization of 2004 and 2012. The biggest common factor number is the GCF number.
So the greatest common factor 2004 and 2012 is 4.

Also check out the Least Common Multiple of 2004 and 2012

Properties of GCF 2004 and 2012

(i) The GCF of 2004 and 2012 is associative

GCF of 2004 and 2012 = GCF of 2012 and 2004

Related Greatest Common Factor of 2004

Related Greatest Common Factor of 2012

Frequently Asked Questions on GCF of 2004 and 2012

1. What is the GCF of 2004 and 2012?

Answer: GCF of 2004 and 2012 is 4.

2. What are the Factors of 2004?

Answer: Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004. There are 12 integers that are factors of 2004. The greatest factor of 2004 is 2004.

3. What are the Factors of 2012?

Answer: Factors of 2012 are 1, 2, 4, 503, 1006, 2012. There are 6 integers that are factors of 2012. The greatest factor of 2012 is 2012.

4. How to Find the GCF of 2004 and 2012?

Answer:

Greatest Common Factor of 2004 and 2012 = 4

Step 1: Find the prime factorization of 2004

2004 = 2 x 2 x 3 x 167

Step 2: Find the prime factorization of 2012

2012 = 2 x 2 x 503

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 2004 and 2012 is 4