What is the Greatest Common Factor of 518 and 523?

Greatest common factor (GCF) of 518 and 523 is 1.

GCF(518,523) = 1

We will now calculate the prime factors of 518 and 523, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 518 and 523.

How to find the GCF of 518 and 523?

We will first find the prime factorization of 518 and 523. After we will calculate the factors of 518 and 523 and find the biggest common factor number .

Step-1: Prime Factorization of 518

Prime factors of 518 are 2, 7, 37. Prime factorization of 518 in exponential form is:

518 = 2¹ × 7¹ × 37¹

Step-2: Prime Factorization of 523

Prime factors of 523 are 523. Prime factorization of 523 in exponential form is:

523 = 523¹

Step-3: Factors of 518

List of positive integer factors of 518 that divides 518 without a remainder.

1, 2, 7, 14, 37, 74, 259

Step-4: Factors of 523

List of positive integer factors of 523 that divides 518 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 518 and 523. The biggest common factor number is the GCF number.
So the greatest common factor 518 and 523 is 1.

Also check out the Least Common Multiple of 518 and 523