What is the Greatest Common Factor of 32364 and 32384?

Greatest common factor (GCF) of 32364 and 32384 is 4.

GCF(32364,32384) = 4

We will now calculate the prime factors of 32364 and 32384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32364 and 32384.

How to find the GCF of 32364 and 32384?

We will first find the prime factorization of 32364 and 32384. After we will calculate the factors of 32364 and 32384 and find the biggest common factor number .

Step-1: Prime Factorization of 32364

Prime factors of 32364 are 2, 3, 29, 31. Prime factorization of 32364 in exponential form is:

32364 = 2² × 3² × 29¹ × 31¹

Step-2: 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-3: Factors of 32364

List of positive integer factors of 32364 that divides 32364 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 29, 31, 36, 58, 62, 87, 93, 116, 124, 174, 186, 261, 279, 348, 372, 522, 558, 899, 1044, 1116, 1798, 2697, 3596, 5394, 8091, 10788, 16182

Step-4: Factors of 32384

List of positive integer factors of 32384 that divides 32364 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32364 and 32384. The biggest common factor number is the GCF number.
So the greatest common factor 32364 and 32384 is 4.

Also check out the Least Common Multiple of 32364 and 32384