What is the Greatest Common Factor of 2500 and 2514?

Greatest common factor (GCF) of 2500 and 2514 is 2.

GCF(2500,2514) = 2

We will now calculate the prime factors of 2500 and 2514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2500 and 2514.

How to find the GCF of 2500 and 2514?

We will first find the prime factorization of 2500 and 2514. After we will calculate the factors of 2500 and 2514 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 2514

Prime factors of 2514 are 2, 3, 419. Prime factorization of 2514 in exponential form is:

2514 = 2¹ × 3¹ × 419¹

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 2514

List of positive integer factors of 2514 that divides 2500 without a remainder.

1, 2, 3, 6, 419, 838, 1257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2500 and 2514. The biggest common factor number is the GCF number.
So the greatest common factor 2500 and 2514 is 2.

Also check out the Least Common Multiple of 2500 and 2514