What is the Greatest Common Factor of 2004 and 2016?

Greatest common factor (GCF) of 2004 and 2016 is 12.

GCF(2004,2016) = 12

We will now calculate the prime factors of 2004 and 2016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2004 and 2016.

How to find the GCF of 2004 and 2016?

We will first find the prime factorization of 2004 and 2016. After we will calculate the factors of 2004 and 2016 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 2016

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

2016 = 2⁵ × 3² × 7¹

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 2016

List of positive integer factors of 2016 that divides 2004 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2004 and 2016. The biggest common factor number is the GCF number.
So the greatest common factor 2004 and 2016 is 12.

Also check out the Least Common Multiple of 2004 and 2016