What is the Greatest Common Factor of 14577 and 14592?

Greatest common factor (GCF) of 14577 and 14592 is 3.

GCF(14577,14592) = 3

We will now calculate the prime factors of 14577 and 14592, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14577 and 14592.

How to find the GCF of 14577 and 14592?

We will first find the prime factorization of 14577 and 14592. After we will calculate the factors of 14577 and 14592 and find the biggest common factor number .

Step-1: Prime Factorization of 14577

Prime factors of 14577 are 3, 43, 113. Prime factorization of 14577 in exponential form is:

14577 = 3¹ × 43¹ × 113¹

Step-2: Prime Factorization of 14592

Prime factors of 14592 are 2, 3, 19. Prime factorization of 14592 in exponential form is:

14592 = 2⁸ × 3¹ × 19¹

Step-3: Factors of 14577

List of positive integer factors of 14577 that divides 14577 without a remainder.

1, 3, 43, 113, 129, 339, 4859

Step-4: Factors of 14592

List of positive integer factors of 14592 that divides 14577 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 128, 152, 192, 228, 256, 304, 384, 456, 608, 768, 912, 1216, 1824, 2432, 3648, 4864, 7296

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14577 and 14592. The biggest common factor number is the GCF number.
So the greatest common factor 14577 and 14592 is 3.

Also check out the Least Common Multiple of 14577 and 14592