What is the Greatest Common Factor of 17296 and 17314?

Greatest common factor (GCF) of 17296 and 17314 is 2.

GCF(17296,17314) = 2

We will now calculate the prime factors of 17296 and 17314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17296 and 17314.

How to find the GCF of 17296 and 17314?

We will first find the prime factorization of 17296 and 17314. After we will calculate the factors of 17296 and 17314 and find the biggest common factor number .

Step-1: Prime Factorization of 17296

Prime factors of 17296 are 2, 23, 47. Prime factorization of 17296 in exponential form is:

17296 = 2⁴ × 23¹ × 47¹

Step-2: 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-3: Factors of 17296

List of positive integer factors of 17296 that divides 17296 without a remainder.

1, 2, 4, 8, 16, 23, 46, 47, 92, 94, 184, 188, 368, 376, 752, 1081, 2162, 4324, 8648

Step-4: Factors of 17314

List of positive integer factors of 17314 that divides 17296 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17296 and 17314. The biggest common factor number is the GCF number.
So the greatest common factor 17296 and 17314 is 2.

Also check out the Least Common Multiple of 17296 and 17314