What is the Greatest Common Factor of 17314 and 17328?

Greatest common factor (GCF) of 17314 and 17328 is 2.

GCF(17314,17328) = 2

We will now calculate the prime factors of 17314 and 17328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17314 and 17328.

How to find the GCF of 17314 and 17328?

We will first find the prime factorization of 17314 and 17328. After we will calculate the factors of 17314 and 17328 and find the biggest common factor number .

Step-1: Prime Factorization of 17314

Prime factors of 17314 are 2, 11, 787. Prime factorization of 17314 in exponential form is:

17314 = 2¹ × 11¹ × 787¹

Step-2: Prime Factorization of 17328

Prime factors of 17328 are 2, 3, 19. Prime factorization of 17328 in exponential form is:

17328 = 2⁴ × 3¹ × 19²

Step-3: Factors of 17314

List of positive integer factors of 17314 that divides 17314 without a remainder.

1, 2, 11, 22, 787, 1574, 8657

Step-4: Factors of 17328

List of positive integer factors of 17328 that divides 17314 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 361, 456, 722, 912, 1083, 1444, 2166, 2888, 4332, 5776, 8664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17314 and 17328. The biggest common factor number is the GCF number.
So the greatest common factor 17314 and 17328 is 2.

Also check out the Least Common Multiple of 17314 and 17328