What is the Greatest Common Factor of 5000 and 5008?

Greatest common factor (GCF) of 5000 and 5008 is 8.

GCF(5000,5008) = 8

We will now calculate the prime factors of 5000 and 5008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5000 and 5008.

How to find the GCF of 5000 and 5008?

We will first find the prime factorization of 5000 and 5008. After we will calculate the factors of 5000 and 5008 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 5008

Prime factors of 5008 are 2, 313. Prime factorization of 5008 in exponential form is:

5008 = 2⁴ × 313¹

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 5008

List of positive integer factors of 5008 that divides 5000 without a remainder.

1, 2, 4, 8, 16, 313, 626, 1252, 2504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5000 and 5008. The biggest common factor number is the GCF number.
So the greatest common factor 5000 and 5008 is 8.

Also check out the Least Common Multiple of 5000 and 5008