What is the Greatest Common Factor of 19200 and 19215?

Greatest common factor (GCF) of 19200 and 19215 is 15.

GCF(19200,19215) = 15

We will now calculate the prime factors of 19200 and 19215, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19200 and 19215.

How to find the GCF of 19200 and 19215?

We will first find the prime factorization of 19200 and 19215. After we will calculate the factors of 19200 and 19215 and find the biggest common factor number .

Step-1: Prime Factorization of 19200

Prime factors of 19200 are 2, 3, 5. Prime factorization of 19200 in exponential form is:

19200 = 2⁸ × 3¹ × 5²

Step-2: Prime Factorization of 19215

Prime factors of 19215 are 3, 5, 7, 61. Prime factorization of 19215 in exponential form is:

19215 = 3² × 5¹ × 7¹ × 61¹

Step-3: Factors of 19200

List of positive integer factors of 19200 that divides 19200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 600, 640, 768, 800, 960, 1200, 1280, 1600, 1920, 2400, 3200, 3840, 4800, 6400, 9600

Step-4: Factors of 19215

List of positive integer factors of 19215 that divides 19200 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 61, 63, 105, 183, 305, 315, 427, 549, 915, 1281, 2135, 2745, 3843, 6405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19200 and 19215. The biggest common factor number is the GCF number.
So the greatest common factor 19200 and 19215 is 15.

Also check out the Least Common Multiple of 19200 and 19215