What is the Greatest Common Factor of 25200 and 25206?

Greatest common factor (GCF) of 25200 and 25206 is 6.

GCF(25200,25206) = 6

We will now calculate the prime factors of 25200 and 25206, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25200 and 25206.

How to find the GCF of 25200 and 25206?

We will first find the prime factorization of 25200 and 25206. After we will calculate the factors of 25200 and 25206 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 25206

Prime factors of 25206 are 2, 3, 4201. Prime factorization of 25206 in exponential form is:

25206 = 2¹ × 3¹ × 4201¹

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 25206

List of positive integer factors of 25206 that divides 25200 without a remainder.

1, 2, 3, 6, 4201, 8402, 12603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25200 and 25206. The biggest common factor number is the GCF number.
So the greatest common factor 25200 and 25206 is 6.

Also check out the Least Common Multiple of 25200 and 25206