What is the Greatest Common Factor of 25200 and 25209?

Greatest common factor (GCF) of 25200 and 25209 is 9.

GCF(25200,25209) = 9

We will now calculate the prime factors of 25200 and 25209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25200 and 25209.

How to find the GCF of 25200 and 25209?

We will first find the prime factorization of 25200 and 25209. After we will calculate the factors of 25200 and 25209 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 25209

Prime factors of 25209 are 3, 2801. Prime factorization of 25209 in exponential form is:

25209 = 3² × 2801¹

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 25209

List of positive integer factors of 25209 that divides 25200 without a remainder.

1, 3, 9, 2801, 8403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25200 and 25209. The biggest common factor number is the GCF number.
So the greatest common factor 25200 and 25209 is 9.

Also check out the Least Common Multiple of 25200 and 25209