What is the Greatest Common Factor of 15200 and 15216?

Greatest common factor (GCF) of 15200 and 15216 is 16.

GCF(15200,15216) = 16

We will now calculate the prime factors of 15200 and 15216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15200 and 15216.

How to find the GCF of 15200 and 15216?

We will first find the prime factorization of 15200 and 15216. After we will calculate the factors of 15200 and 15216 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 15216

Prime factors of 15216 are 2, 3, 317. Prime factorization of 15216 in exponential form is:

15216 = 2⁴ × 3¹ × 317¹

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 15216

List of positive integer factors of 15216 that divides 15200 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 317, 634, 951, 1268, 1902, 2536, 3804, 5072, 7608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15200 and 15216. The biggest common factor number is the GCF number.
So the greatest common factor 15200 and 15216 is 16.

Also check out the Least Common Multiple of 15200 and 15216