What is the Greatest Common Factor of 25186 and 25200?

Greatest common factor (GCF) of 25186 and 25200 is 14.

GCF(25186,25200) = 14

We will now calculate the prime factors of 25186 and 25200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25186 and 25200.

How to find the GCF of 25186 and 25200?

We will first find the prime factorization of 25186 and 25200. After we will calculate the factors of 25186 and 25200 and find the biggest common factor number .

Step-1: Prime Factorization of 25186

Prime factors of 25186 are 2, 7, 257. Prime factorization of 25186 in exponential form is:

25186 = 2¹ × 7² × 257¹

Step-2: 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-3: Factors of 25186

List of positive integer factors of 25186 that divides 25186 without a remainder.

1, 2, 7, 14, 49, 98, 257, 514, 1799, 3598, 12593

Step-4: Factors of 25200

List of positive integer factors of 25200 that divides 25186 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25186 and 25200. The biggest common factor number is the GCF number.
So the greatest common factor 25186 and 25200 is 14.

Also check out the Least Common Multiple of 25186 and 25200