What is the Greatest Common Factor of 15314 and 15328?

Greatest common factor (GCF) of 15314 and 15328 is 2.

GCF(15314,15328) = 2

We will now calculate the prime factors of 15314 and 15328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15314 and 15328.

How to find the GCF of 15314 and 15328?

We will first find the prime factorization of 15314 and 15328. After we will calculate the factors of 15314 and 15328 and find the biggest common factor number .

Step-1: Prime Factorization of 15314

Prime factors of 15314 are 2, 13, 19, 31. Prime factorization of 15314 in exponential form is:

15314 = 2¹ × 13¹ × 19¹ × 31¹

Step-2: Prime Factorization of 15328

Prime factors of 15328 are 2, 479. Prime factorization of 15328 in exponential form is:

15328 = 2⁵ × 479¹

Step-3: Factors of 15314

List of positive integer factors of 15314 that divides 15314 without a remainder.

1, 2, 13, 19, 26, 31, 38, 62, 247, 403, 494, 589, 806, 1178, 7657

Step-4: Factors of 15328

List of positive integer factors of 15328 that divides 15314 without a remainder.

1, 2, 4, 8, 16, 32, 479, 958, 1916, 3832, 7664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15314 and 15328. The biggest common factor number is the GCF number.
So the greatest common factor 15314 and 15328 is 2.

Also check out the Least Common Multiple of 15314 and 15328