What is the Greatest Common Factor of 15306 and 15312?

Greatest common factor (GCF) of 15306 and 15312 is 6.

GCF(15306,15312) = 6

We will now calculate the prime factors of 15306 and 15312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15306 and 15312.

How to find the GCF of 15306 and 15312?

We will first find the prime factorization of 15306 and 15312. After we will calculate the factors of 15306 and 15312 and find the biggest common factor number .

Step-1: Prime Factorization of 15306

Prime factors of 15306 are 2, 3, 2551. Prime factorization of 15306 in exponential form is:

15306 = 2¹ × 3¹ × 2551¹

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 15306

List of positive integer factors of 15306 that divides 15306 without a remainder.

1, 2, 3, 6, 2551, 5102, 7653

Step-4: Factors of 15312

List of positive integer factors of 15312 that divides 15306 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 15306 and 15312. The biggest common factor number is the GCF number.
So the greatest common factor 15306 and 15312 is 6.

Also check out the Least Common Multiple of 15306 and 15312