What is the Greatest Common Factor of 14496 and 14512?

Greatest common factor (GCF) of 14496 and 14512 is 16.

GCF(14496,14512) = 16

We will now calculate the prime factors of 14496 and 14512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14496 and 14512.

How to find the GCF of 14496 and 14512?

We will first find the prime factorization of 14496 and 14512. After we will calculate the factors of 14496 and 14512 and find the biggest common factor number .

Step-1: Prime Factorization of 14496

Prime factors of 14496 are 2, 3, 151. Prime factorization of 14496 in exponential form is:

14496 = 2⁵ × 3¹ × 151¹

Step-2: Prime Factorization of 14512

Prime factors of 14512 are 2, 907. Prime factorization of 14512 in exponential form is:

14512 = 2⁴ × 907¹

Step-3: Factors of 14496

List of positive integer factors of 14496 that divides 14496 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 151, 302, 453, 604, 906, 1208, 1812, 2416, 3624, 4832, 7248

Step-4: Factors of 14512

List of positive integer factors of 14512 that divides 14496 without a remainder.

1, 2, 4, 8, 16, 907, 1814, 3628, 7256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14496 and 14512. The biggest common factor number is the GCF number.
So the greatest common factor 14496 and 14512 is 16.

Also check out the Least Common Multiple of 14496 and 14512