What is the Greatest Common Factor of 512 and 517?

Greatest common factor (GCF) of 512 and 517 is 1.

GCF(512,517) = 1

We will now calculate the prime factors of 512 and 517, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 512 and 517.

How to find the GCF of 512 and 517?

We will first find the prime factorization of 512 and 517. After we will calculate the factors of 512 and 517 and find the biggest common factor number .

Step-1: Prime Factorization of 512

Prime factors of 512 are 2. Prime factorization of 512 in exponential form is:

512 = 2⁹

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 512

List of positive integer factors of 512 that divides 512 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 256

Step-4: Factors of 517

List of positive integer factors of 517 that divides 512 without a remainder.

1, 11, 47

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 512 and 517. The biggest common factor number is the GCF number.
So the greatest common factor 512 and 517 is 1.

Also check out the Least Common Multiple of 512 and 517