What is the Greatest Common Factor of 67200 and 67215?

Greatest common factor (GCF) of 67200 and 67215 is 15.

GCF(67200,67215) = 15

We will now calculate the prime factors of 67200 and 67215, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67200 and 67215.

How to find the GCF of 67200 and 67215?

We will first find the prime factorization of 67200 and 67215. After we will calculate the factors of 67200 and 67215 and find the biggest common factor number .

Step-1: Prime Factorization of 67200

Prime factors of 67200 are 2, 3, 5, 7. Prime factorization of 67200 in exponential form is:

67200 = 2⁷ × 3¹ × 5² × 7¹

Step-2: Prime Factorization of 67215

Prime factors of 67215 are 3, 5, 4481. Prime factorization of 67215 in exponential form is:

67215 = 3¹ × 5¹ × 4481¹

Step-3: Factors of 67200

List of positive integer factors of 67200 that divides 67200 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 128, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 384, 400, 420, 448, 480, 525, 560, 600, 640, 672, 700, 800, 840, 896, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 1920, 2100, 2240, 2400, 2688, 2800, 3200, 3360, 4200, 4480, 4800, 5600, 6720, 8400, 9600, 11200, 13440, 16800, 22400, 33600

Step-4: Factors of 67215

List of positive integer factors of 67215 that divides 67200 without a remainder.

1, 3, 5, 15, 4481, 13443, 22405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67200 and 67215. The biggest common factor number is the GCF number.
So the greatest common factor 67200 and 67215 is 15.

Also check out the Least Common Multiple of 67200 and 67215