What is the Greatest Common Factor of 43200 and 43205?

Greatest common factor (GCF) of 43200 and 43205 is 5.

GCF(43200,43205) = 5

We will now calculate the prime factors of 43200 and 43205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43200 and 43205.

How to find the GCF of 43200 and 43205?

We will first find the prime factorization of 43200 and 43205. After we will calculate the factors of 43200 and 43205 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 43205

Prime factors of 43205 are 5, 8641. Prime factorization of 43205 in exponential form is:

43205 = 5¹ × 8641¹

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 43205

List of positive integer factors of 43205 that divides 43200 without a remainder.

1, 5, 8641

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43200 and 43205. The biggest common factor number is the GCF number.
So the greatest common factor 43200 and 43205 is 5.

Also check out the Least Common Multiple of 43200 and 43205