What is the Greatest Common Factor of 43200 and 43215?

Greatest common factor (GCF) of 43200 and 43215 is 15.

GCF(43200,43215) = 15

We will now calculate the prime factors of 43200 and 43215, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43200 and 43215.

How to find the GCF of 43200 and 43215?

We will first find the prime factorization of 43200 and 43215. After we will calculate the factors of 43200 and 43215 and find the biggest common factor number .

Step-1: Prime Factorization of 43200

Prime factors of 43200 are 2, 3, 5. Prime factorization of 43200 in exponential form is:

43200 = 2⁶ × 3³ × 5²

Step-2: Prime Factorization of 43215

Prime factors of 43215 are 3, 5, 43, 67. Prime factorization of 43215 in exponential form is:

43215 = 3¹ × 5¹ × 43¹ × 67¹

Step-3: Factors of 43200

List of positive integer factors of 43200 that divides 43200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 192, 200, 216, 225, 240, 270, 288, 300, 320, 360, 400, 432, 450, 480, 540, 576, 600, 675, 720, 800, 864, 900, 960, 1080, 1200, 1350, 1440, 1600, 1728, 1800, 2160, 2400, 2700, 2880, 3600, 4320, 4800, 5400, 7200, 8640, 10800, 14400, 21600

Step-4: Factors of 43215

List of positive integer factors of 43215 that divides 43200 without a remainder.

1, 3, 5, 15, 43, 67, 129, 201, 215, 335, 645, 1005, 2881, 8643, 14405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43200 and 43215. The biggest common factor number is the GCF number.
So the greatest common factor 43200 and 43215 is 15.

Also check out the Least Common Multiple of 43200 and 43215