What is the Greatest Common Factor of 43584 and 43600?

Greatest common factor (GCF) of 43584 and 43600 is 16.

GCF(43584,43600) = 16

We will now calculate the prime factors of 43584 and 43600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43584 and 43600.

How to find the GCF of 43584 and 43600?

We will first find the prime factorization of 43584 and 43600. After we will calculate the factors of 43584 and 43600 and find the biggest common factor number .

Step-1: Prime Factorization of 43584

Prime factors of 43584 are 2, 3, 227. Prime factorization of 43584 in exponential form is:

43584 = 2⁶ × 3¹ × 227¹

Step-2: Prime Factorization of 43600

Prime factors of 43600 are 2, 5, 109. Prime factorization of 43600 in exponential form is:

43600 = 2⁴ × 5² × 109¹

Step-3: Factors of 43584

List of positive integer factors of 43584 that divides 43584 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 227, 454, 681, 908, 1362, 1816, 2724, 3632, 5448, 7264, 10896, 14528, 21792

Step-4: Factors of 43600

List of positive integer factors of 43600 that divides 43584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 109, 200, 218, 400, 436, 545, 872, 1090, 1744, 2180, 2725, 4360, 5450, 8720, 10900, 21800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43584 and 43600. The biggest common factor number is the GCF number.
So the greatest common factor 43584 and 43600 is 16.

Also check out the Least Common Multiple of 43584 and 43600