What is the Greatest Common Factor of 25200 and 25214?

Greatest common factor (GCF) of 25200 and 25214 is 14.

GCF(25200,25214) = 14

We will now calculate the prime factors of 25200 and 25214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25200 and 25214.

How to find the GCF of 25200 and 25214?

We will first find the prime factorization of 25200 and 25214. After we will calculate the factors of 25200 and 25214 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 25214

Prime factors of 25214 are 2, 7, 1801. Prime factorization of 25214 in exponential form is:

25214 = 2¹ × 7¹ × 1801¹

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 25214

List of positive integer factors of 25214 that divides 25200 without a remainder.

1, 2, 7, 14, 1801, 3602, 12607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25200 and 25214. The biggest common factor number is the GCF number.
So the greatest common factor 25200 and 25214 is 14.

Also check out the Least Common Multiple of 25200 and 25214