What is the Greatest Common Factor of 1984 and 2004?

Greatest common factor (GCF) of 1984 and 2004 is 4.

GCF(1984,2004) = 4

We will now calculate the prime factors of 1984 and 2004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1984 and 2004.

How to find the GCF of 1984 and 2004?

We will first find the prime factorization of 1984 and 2004. After we will calculate the factors of 1984 and 2004 and find the biggest common factor number .

Step-1: Prime Factorization of 1984

Prime factors of 1984 are 2, 31. Prime factorization of 1984 in exponential form is:

1984 = 2⁶ × 31¹

Step-2: 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-3: Factors of 1984

List of positive integer factors of 1984 that divides 1984 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992

Step-4: Factors of 2004

List of positive integer factors of 2004 that divides 1984 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1984 and 2004. The biggest common factor number is the GCF number.
So the greatest common factor 1984 and 2004 is 4.

Also check out the Least Common Multiple of 1984 and 2004