What is the Greatest Common Factor of 15200 and 15209?

Greatest common factor (GCF) of 15200 and 15209 is 1.

GCF(15200,15209) = 1

We will now calculate the prime factors of 15200 and 15209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15200 and 15209.

How to find the GCF of 15200 and 15209?

We will first find the prime factorization of 15200 and 15209. After we will calculate the factors of 15200 and 15209 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 15209

Prime factors of 15209 are 67, 227. Prime factorization of 15209 in exponential form is:

15209 = 67¹ × 227¹

Step-3: Factors of 15200

List of positive integer factors of 15200 that divides 15200 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

Step-4: Factors of 15209

List of positive integer factors of 15209 that divides 15200 without a remainder.

1, 67, 227

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15200 and 15209. The biggest common factor number is the GCF number.
So the greatest common factor 15200 and 15209 is 1.

Also check out the Least Common Multiple of 15200 and 15209