What is the Greatest Common Factor of 43188 and 43200?

Greatest common factor (GCF) of 43188 and 43200 is 12.

GCF(43188,43200) = 12

We will now calculate the prime factors of 43188 and 43200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43188 and 43200.

How to find the GCF of 43188 and 43200?

We will first find the prime factorization of 43188 and 43200. After we will calculate the factors of 43188 and 43200 and find the biggest common factor number .

Step-1: Prime Factorization of 43188

Prime factors of 43188 are 2, 3, 59, 61. Prime factorization of 43188 in exponential form is:

43188 = 2² × 3¹ × 59¹ × 61¹

Step-2: 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-3: Factors of 43188

List of positive integer factors of 43188 that divides 43188 without a remainder.

1, 2, 3, 4, 6, 12, 59, 61, 118, 122, 177, 183, 236, 244, 354, 366, 708, 732, 3599, 7198, 10797, 14396, 21594

Step-4: Factors of 43200

List of positive integer factors of 43200 that divides 43188 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43188 and 43200. The biggest common factor number is the GCF number.
So the greatest common factor 43188 and 43200 is 12.

Also check out the Least Common Multiple of 43188 and 43200