What is the Greatest Common Factor of 1000 and 1004?

Greatest common factor (GCF) of 1000 and 1004 is 4.

GCF(1000,1004) = 4

We will now calculate the prime factors of 1000 and 1004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1000 and 1004.

How to find the GCF of 1000 and 1004?

We will first find the prime factorization of 1000 and 1004. After we will calculate the factors of 1000 and 1004 and find the biggest common factor number .

Step-1: Prime Factorization of 1000

Prime factors of 1000 are 2, 5. Prime factorization of 1000 in exponential form is:

1000 = 2³ × 5³

Step-2: Prime Factorization of 1004

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

1004 = 2² × 251¹

Step-3: Factors of 1000

List of positive integer factors of 1000 that divides 1000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500

Step-4: Factors of 1004

List of positive integer factors of 1004 that divides 1000 without a remainder.

1, 2, 4, 251, 502

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1000 and 1004. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1004 is 4.

Also check out the Least Common Multiple of 1000 and 1004