What is the Greatest Common Factor of 2004 and 2014?

Greatest common factor (GCF) of 2004 and 2014 is 2.

GCF(2004,2014) = 2

We will now calculate the prime factors of 2004 and 2014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2004 and 2014.

How to find the GCF of 2004 and 2014?

We will first find the prime factorization of 2004 and 2014. After we will calculate the factors of 2004 and 2014 and find the biggest common factor number .

Step-1: Prime Factorization of 2004

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

2004 = 2² × 3¹ × 167¹

Step-2: Prime Factorization of 2014

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

2014 = 2¹ × 19¹ × 53¹

Step-3: 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

Step-4: Factors of 2014

List of positive integer factors of 2014 that divides 2004 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2004 and 2014. The biggest common factor number is the GCF number.
So the greatest common factor 2004 and 2014 is 2.

Also check out the Least Common Multiple of 2004 and 2014