What is the Greatest Common Factor of 2500 and 2520?

Greatest common factor (GCF) of 2500 and 2520 is 20.

GCF(2500,2520) = 20

We will now calculate the prime factors of 2500 and 2520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2500 and 2520.

How to find the GCF of 2500 and 2520?

We will first find the prime factorization of 2500 and 2520. After we will calculate the factors of 2500 and 2520 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 2520

Prime factors of 2520 are 2, 3, 5, 7. Prime factorization of 2520 in exponential form is:

2520 = 2³ × 3² × 5¹ × 7¹

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 2520

List of positive integer factors of 2520 that divides 2500 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2500 and 2520. The biggest common factor number is the GCF number.
So the greatest common factor 2500 and 2520 is 20.

Also check out the Least Common Multiple of 2500 and 2520