What is the Greatest Common Factor of 17297 and 17313?

Greatest common factor (GCF) of 17297 and 17313 is 1.

GCF(17297,17313) = 1

We will now calculate the prime factors of 17297 and 17313, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17297 and 17313.

How to find the GCF of 17297 and 17313?

We will first find the prime factorization of 17297 and 17313. After we will calculate the factors of 17297 and 17313 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 17313

Prime factors of 17313 are 3, 29, 199. Prime factorization of 17313 in exponential form is:

17313 = 3¹ × 29¹ × 199¹

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 17313

List of positive integer factors of 17313 that divides 17297 without a remainder.

1, 3, 29, 87, 199, 597, 5771

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17297 and 17313. The biggest common factor number is the GCF number.
So the greatest common factor 17297 and 17313 is 1.

Also check out the Least Common Multiple of 17297 and 17313