What is the Greatest Common Factor of 43200 and 43212?

Greatest common factor (GCF) of 43200 and 43212 is 12.

GCF(43200,43212) = 12

We will now calculate the prime factors of 43200 and 43212, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43200 and 43212.

How to find the GCF of 43200 and 43212?

We will first find the prime factorization of 43200 and 43212. After we will calculate the factors of 43200 and 43212 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 43212

Prime factors of 43212 are 2, 3, 13, 277. Prime factorization of 43212 in exponential form is:

43212 = 2² × 3¹ × 13¹ × 277¹

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 43212

List of positive integer factors of 43212 that divides 43200 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 277, 554, 831, 1108, 1662, 3324, 3601, 7202, 10803, 14404, 21606

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43200 and 43212. The biggest common factor number is the GCF number.
So the greatest common factor 43200 and 43212 is 12.

Also check out the Least Common Multiple of 43200 and 43212