What is the Greatest Common Factor of 15296 and 15312?

Greatest common factor (GCF) of 15296 and 15312 is 16.

GCF(15296,15312) = 16

We will now calculate the prime factors of 15296 and 15312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15296 and 15312.

How to find the GCF of 15296 and 15312?

We will first find the prime factorization of 15296 and 15312. After we will calculate the factors of 15296 and 15312 and find the biggest common factor number .

Step-1: Prime Factorization of 15296

Prime factors of 15296 are 2, 239. Prime factorization of 15296 in exponential form is:

15296 = 2⁶ × 239¹

Step-2: Prime Factorization of 15312

Prime factors of 15312 are 2, 3, 11, 29. Prime factorization of 15312 in exponential form is:

15312 = 2⁴ × 3¹ × 11¹ × 29¹

Step-3: Factors of 15296

List of positive integer factors of 15296 that divides 15296 without a remainder.

1, 2, 4, 8, 16, 32, 64, 239, 478, 956, 1912, 3824, 7648

Step-4: Factors of 15312

List of positive integer factors of 15312 that divides 15296 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 29, 33, 44, 48, 58, 66, 87, 88, 116, 132, 174, 176, 232, 264, 319, 348, 464, 528, 638, 696, 957, 1276, 1392, 1914, 2552, 3828, 5104, 7656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15296 and 15312. The biggest common factor number is the GCF number.
So the greatest common factor 15296 and 15312 is 16.

Also check out the Least Common Multiple of 15296 and 15312