What is the Greatest Common Factor of 2500 and 2510?

Greatest common factor (GCF) of 2500 and 2510 is 10.

GCF(2500,2510) = 10

We will now calculate the prime factors of 2500 and 2510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2500 and 2510.

How to find the GCF of 2500 and 2510?

We will first find the prime factorization of 2500 and 2510. After we will calculate the factors of 2500 and 2510 and find the biggest common factor number .

Step-1: Prime Factorization of 2500

Prime factors of 2500 are 2, 5. Prime factorization of 2500 in exponential form is:

2500 = 2² × 5⁴

Step-2: Prime Factorization of 2510

Prime factors of 2510 are 2, 5, 251. Prime factorization of 2510 in exponential form is:

2510 = 2¹ × 5¹ × 251¹

Step-3: Factors of 2500

List of positive integer factors of 2500 that divides 2500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250

Step-4: Factors of 2510

List of positive integer factors of 2510 that divides 2500 without a remainder.

1, 2, 5, 10, 251, 502, 1255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2500 and 2510. The biggest common factor number is the GCF number.
So the greatest common factor 2500 and 2510 is 10.

Also check out the Least Common Multiple of 2500 and 2510