What is the Greatest Common Factor of 5000 and 5004?

Greatest common factor (GCF) of 5000 and 5004 is 4.

GCF(5000,5004) = 4

We will now calculate the prime factors of 5000 and 5004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5000 and 5004.

How to find the GCF of 5000 and 5004?

We will first find the prime factorization of 5000 and 5004. After we will calculate the factors of 5000 and 5004 and find the biggest common factor number .

Step-1: Prime Factorization of 5000

Prime factors of 5000 are 2, 5. Prime factorization of 5000 in exponential form is:

5000 = 2³ × 5⁴

Step-2: Prime Factorization of 5004

Prime factors of 5004 are 2, 3, 139. Prime factorization of 5004 in exponential form is:

5004 = 2² × 3² × 139¹

Step-3: Factors of 5000

List of positive integer factors of 5000 that divides 5000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500

Step-4: Factors of 5004

List of positive integer factors of 5004 that divides 5000 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 139, 278, 417, 556, 834, 1251, 1668, 2502

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5000 and 5004. The biggest common factor number is the GCF number.
So the greatest common factor 5000 and 5004 is 4.

Also check out the Least Common Multiple of 5000 and 5004