What is the Greatest Common Factor of 25200 and 25217?

Greatest common factor (GCF) of 25200 and 25217 is 1.

GCF(25200,25217) = 1

We will now calculate the prime factors of 25200 and 25217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25200 and 25217.

How to find the GCF of 25200 and 25217?

We will first find the prime factorization of 25200 and 25217. After we will calculate the factors of 25200 and 25217 and find the biggest common factor number .

Step-1: Prime Factorization of 25200

Prime factors of 25200 are 2, 3, 5, 7. Prime factorization of 25200 in exponential form is:

25200 = 2⁴ × 3² × 5² × 7¹

Step-2: Prime Factorization of 25217

Prime factors of 25217 are 151, 167. Prime factorization of 25217 in exponential form is:

25217 = 151¹ × 167¹

Step-3: Factors of 25200

List of positive integer factors of 25200 that divides 25200 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 100, 105, 112, 120, 126, 140, 144, 150, 168, 175, 180, 200, 210, 225, 240, 252, 280, 300, 315, 336, 350, 360, 400, 420, 450, 504, 525, 560, 600, 630, 700, 720, 840, 900, 1008, 1050, 1200, 1260, 1400, 1575, 1680, 1800, 2100, 2520, 2800, 3150, 3600, 4200, 5040, 6300, 8400, 12600

Step-4: Factors of 25217

List of positive integer factors of 25217 that divides 25200 without a remainder.

1, 151, 167

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25200 and 25217. The biggest common factor number is the GCF number.
So the greatest common factor 25200 and 25217 is 1.

Also check out the Least Common Multiple of 25200 and 25217