What is the Greatest Common Factor of 15200 and 15219?

Greatest common factor (GCF) of 15200 and 15219 is 19.

GCF(15200,15219) = 19

We will now calculate the prime factors of 15200 and 15219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15200 and 15219.

How to find the GCF of 15200 and 15219?

We will first find the prime factorization of 15200 and 15219. After we will calculate the factors of 15200 and 15219 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 15219

Prime factors of 15219 are 3, 19, 89. Prime factorization of 15219 in exponential form is:

15219 = 3² × 19¹ × 89¹

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 15219

List of positive integer factors of 15219 that divides 15200 without a remainder.

1, 3, 9, 19, 57, 89, 171, 267, 801, 1691, 5073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15200 and 15219. The biggest common factor number is the GCF number.
So the greatest common factor 15200 and 15219 is 19.

Also check out the Least Common Multiple of 15200 and 15219