What is the Greatest Common Factor of 509 and 517?

Greatest common factor (GCF) of 509 and 517 is 1.

GCF(509,517) = 1

We will now calculate the prime factors of 509 and 517, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 509 and 517.

How to find the GCF of 509 and 517?

We will first find the prime factorization of 509 and 517. After we will calculate the factors of 509 and 517 and find the biggest common factor number .

Step-1: Prime Factorization of 509

Prime factors of 509 are 509. Prime factorization of 509 in exponential form is:

509 = 509¹

Step-2: Prime Factorization of 517

Prime factors of 517 are 11, 47. Prime factorization of 517 in exponential form is:

517 = 11¹ × 47¹

Step-3: Factors of 509

List of positive integer factors of 509 that divides 509 without a remainder.

Step-4: Factors of 517

List of positive integer factors of 517 that divides 509 without a remainder.

1, 11, 47

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 509 and 517. The biggest common factor number is the GCF number.
So the greatest common factor 509 and 517 is 1.

Also check out the Least Common Multiple of 509 and 517