What is the Greatest Common Factor of 17297 and 17312?

Greatest common factor (GCF) of 17297 and 17312 is 1.

GCF(17297,17312) = 1

We will now calculate the prime factors of 17297 and 17312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17297 and 17312.

How to find the GCF of 17297 and 17312?

We will first find the prime factorization of 17297 and 17312. After we will calculate the factors of 17297 and 17312 and find the biggest common factor number .

Step-1: Prime Factorization of 17297

Prime factors of 17297 are 7, 353. Prime factorization of 17297 in exponential form is:

17297 = 7² × 353¹

Step-2: Prime Factorization of 17312

Prime factors of 17312 are 2, 541. Prime factorization of 17312 in exponential form is:

17312 = 2⁵ × 541¹

Step-3: Factors of 17297

List of positive integer factors of 17297 that divides 17297 without a remainder.

1, 7, 49, 353, 2471

Step-4: Factors of 17312

List of positive integer factors of 17312 that divides 17297 without a remainder.

1, 2, 4, 8, 16, 32, 541, 1082, 2164, 4328, 8656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17297 and 17312. The biggest common factor number is the GCF number.
So the greatest common factor 17297 and 17312 is 1.

Also check out the Least Common Multiple of 17297 and 17312