What is the Greatest Common Factor of 32384 and 32400?

Greatest common factor (GCF) of 32384 and 32400 is 16.

GCF(32384,32400) = 16

We will now calculate the prime factors of 32384 and 32400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32384 and 32400.

How to find the GCF of 32384 and 32400?

We will first find the prime factorization of 32384 and 32400. After we will calculate the factors of 32384 and 32400 and find the biggest common factor number .

Step-1: Prime Factorization of 32384

Prime factors of 32384 are 2, 11, 23. Prime factorization of 32384 in exponential form is:

32384 = 2⁷ × 11¹ × 23¹

Step-2: Prime Factorization of 32400

Prime factors of 32400 are 2, 3, 5. Prime factorization of 32400 in exponential form is:

32400 = 2⁴ × 3⁴ × 5²

Step-3: Factors of 32384

List of positive integer factors of 32384 that divides 32384 without a remainder.

1, 2, 4, 8, 11, 16, 22, 23, 32, 44, 46, 64, 88, 92, 128, 176, 184, 253, 352, 368, 506, 704, 736, 1012, 1408, 1472, 2024, 2944, 4048, 8096, 16192

Step-4: Factors of 32400

List of positive integer factors of 32400 that divides 32384 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32384 and 32400. The biggest common factor number is the GCF number.
So the greatest common factor 32384 and 32400 is 16.

Also check out the Least Common Multiple of 32384 and 32400