What is the Greatest Common Factor of 1004 and 1008?

Greatest common factor (GCF) of 1004 and 1008 is 4.

GCF(1004,1008) = 4

We will now calculate the prime factors of 1004 and 1008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1004 and 1008.

How to find the GCF of 1004 and 1008?

We will first find the prime factorization of 1004 and 1008. After we will calculate the factors of 1004 and 1008 and find the biggest common factor number .

Step-1: Prime Factorization of 1004

Prime factors of 1004 are 2, 251. Prime factorization of 1004 in exponential form is:

1004 = 2² × 251¹

Step-2: Prime Factorization of 1008

Prime factors of 1008 are 2, 3, 7. Prime factorization of 1008 in exponential form is:

1008 = 2⁴ × 3² × 7¹

Step-3: Factors of 1004

List of positive integer factors of 1004 that divides 1004 without a remainder.

1, 2, 4, 251, 502

Step-4: Factors of 1008

List of positive integer factors of 1008 that divides 1004 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1004 and 1008. The biggest common factor number is the GCF number.
So the greatest common factor 1004 and 1008 is 4.

Also check out the Least Common Multiple of 1004 and 1008