What is the Greatest Common Factor of 15186 and 15200?

Greatest common factor (GCF) of 15186 and 15200 is 2.

GCF(15186,15200) = 2

We will now calculate the prime factors of 15186 and 15200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15186 and 15200.

How to find the GCF of 15186 and 15200?

We will first find the prime factorization of 15186 and 15200. After we will calculate the factors of 15186 and 15200 and find the biggest common factor number .

Step-1: Prime Factorization of 15186

Prime factors of 15186 are 2, 3, 2531. Prime factorization of 15186 in exponential form is:

15186 = 2¹ × 3¹ × 2531¹

Step-2: Prime Factorization of 15200

Prime factors of 15200 are 2, 5, 19. Prime factorization of 15200 in exponential form is:

15200 = 2⁵ × 5² × 19¹

Step-3: Factors of 15186

List of positive integer factors of 15186 that divides 15186 without a remainder.

1, 2, 3, 6, 2531, 5062, 7593

Step-4: Factors of 15200

List of positive integer factors of 15200 that divides 15186 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 32, 38, 40, 50, 76, 80, 95, 100, 152, 160, 190, 200, 304, 380, 400, 475, 608, 760, 800, 950, 1520, 1900, 3040, 3800, 7600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15186 and 15200. The biggest common factor number is the GCF number.
So the greatest common factor 15186 and 15200 is 2.

Also check out the Least Common Multiple of 15186 and 15200