What is the Greatest Common Factor of 5000 and 5010?

Greatest common factor (GCF) of 5000 and 5010 is 10.

GCF(5000,5010) = 10

We will now calculate the prime factors of 5000 and 5010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5000 and 5010.

How to find the GCF of 5000 and 5010?

We will first find the prime factorization of 5000 and 5010. After we will calculate the factors of 5000 and 5010 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 5010

Prime factors of 5010 are 2, 3, 5, 167. Prime factorization of 5010 in exponential form is:

5010 = 2¹ × 3¹ × 5¹ × 167¹

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 5010

List of positive integer factors of 5010 that divides 5000 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 167, 334, 501, 835, 1002, 1670, 2505

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5000 and 5010. The biggest common factor number is the GCF number.
So the greatest common factor 5000 and 5010 is 10.

Also check out the Least Common Multiple of 5000 and 5010