What is the Greatest Common Factor of 2500 and 2509?

Greatest common factor (GCF) of 2500 and 2509 is 1.

GCF(2500,2509) = 1

We will now calculate the prime factors of 2500 and 2509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2500 and 2509.

How to find the GCF of 2500 and 2509?

We will first find the prime factorization of 2500 and 2509. After we will calculate the factors of 2500 and 2509 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 2509

Prime factors of 2509 are 13, 193. Prime factorization of 2509 in exponential form is:

2509 = 13¹ × 193¹

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 2509

List of positive integer factors of 2509 that divides 2500 without a remainder.

1, 13, 193

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2500 and 2509. The biggest common factor number is the GCF number.
So the greatest common factor 2500 and 2509 is 1.

Also check out the Least Common Multiple of 2500 and 2509