What is the Greatest Common Factor of 5000 and 5005?

Greatest common factor (GCF) of 5000 and 5005 is 5.

GCF(5000,5005) = 5

We will now calculate the prime factors of 5000 and 5005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5000 and 5005.

How to find the GCF of 5000 and 5005?

We will first find the prime factorization of 5000 and 5005. After we will calculate the factors of 5000 and 5005 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 5005

Prime factors of 5005 are 5, 7, 11, 13. Prime factorization of 5005 in exponential form is:

5005 = 5¹ × 7¹ × 11¹ × 13¹

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 5005

List of positive integer factors of 5005 that divides 5000 without a remainder.

1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5000 and 5005. The biggest common factor number is the GCF number.
So the greatest common factor 5000 and 5005 is 5.

Also check out the Least Common Multiple of 5000 and 5005