What is the Greatest Common Factor of 25500 and 25517?

Greatest common factor (GCF) of 25500 and 25517 is 17.

GCF(25500,25517) = 17

We will now calculate the prime factors of 25500 and 25517, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25500 and 25517.

How to find the GCF of 25500 and 25517?

We will first find the prime factorization of 25500 and 25517. After we will calculate the factors of 25500 and 25517 and find the biggest common factor number .

Step-1: Prime Factorization of 25500

Prime factors of 25500 are 2, 3, 5, 17. Prime factorization of 25500 in exponential form is:

25500 = 2² × 3¹ × 5³ × 17¹

Step-2: Prime Factorization of 25517

Prime factors of 25517 are 17, 19, 79. Prime factorization of 25517 in exponential form is:

25517 = 17¹ × 19¹ × 79¹

Step-3: Factors of 25500

List of positive integer factors of 25500 that divides 25500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 50, 51, 60, 68, 75, 85, 100, 102, 125, 150, 170, 204, 250, 255, 300, 340, 375, 425, 500, 510, 750, 850, 1020, 1275, 1500, 1700, 2125, 2550, 4250, 5100, 6375, 8500, 12750

Step-4: Factors of 25517

List of positive integer factors of 25517 that divides 25500 without a remainder.

1, 17, 19, 79, 323, 1343, 1501

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25500 and 25517. The biggest common factor number is the GCF number.
So the greatest common factor 25500 and 25517 is 17.

Also check out the Least Common Multiple of 25500 and 25517