What is the Greatest Common Factor of 506 and 522?

Greatest common factor (GCF) of 506 and 522 is 2.

GCF(506,522) = 2

We will now calculate the prime factors of 506 and 522, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 506 and 522.

How to find the GCF of 506 and 522?

We will first find the prime factorization of 506 and 522. After we will calculate the factors of 506 and 522 and find the biggest common factor number .

Step-1: Prime Factorization of 506

Prime factors of 506 are 2, 11, 23. Prime factorization of 506 in exponential form is:

506 = 2¹ × 11¹ × 23¹

Step-2: Prime Factorization of 522

Prime factors of 522 are 2, 3, 29. Prime factorization of 522 in exponential form is:

522 = 2¹ × 3² × 29¹

Step-3: Factors of 506

List of positive integer factors of 506 that divides 506 without a remainder.

1, 2, 11, 22, 23, 46, 253

Step-4: Factors of 522

List of positive integer factors of 522 that divides 506 without a remainder.

1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 506 and 522. The biggest common factor number is the GCF number.
So the greatest common factor 506 and 522 is 2.

Also check out the Least Common Multiple of 506 and 522