What is the Greatest Common Factor of 43200 and 43204?

Greatest common factor (GCF) of 43200 and 43204 is 4.

GCF(43200,43204) = 4

We will now calculate the prime factors of 43200 and 43204, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43200 and 43204.

How to find the GCF of 43200 and 43204?

We will first find the prime factorization of 43200 and 43204. After we will calculate the factors of 43200 and 43204 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 43204

Prime factors of 43204 are 2, 7, 1543. Prime factorization of 43204 in exponential form is:

43204 = 2² × 7¹ × 1543¹

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 43204

List of positive integer factors of 43204 that divides 43200 without a remainder.

1, 2, 4, 7, 14, 28, 1543, 3086, 6172, 10801, 21602

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43200 and 43204. The biggest common factor number is the GCF number.
So the greatest common factor 43200 and 43204 is 4.

Also check out the Least Common Multiple of 43200 and 43204