What is the Greatest Common Factor of 522 and 538?

Greatest common factor (GCF) of 522 and 538 is 2.

GCF(522,538) = 2

We will now calculate the prime factors of 522 and 538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 522 and 538.

How to find the GCF of 522 and 538?

We will first find the prime factorization of 522 and 538. After we will calculate the factors of 522 and 538 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 538

Prime factors of 538 are 2, 269. Prime factorization of 538 in exponential form is:

538 = 2¹ × 269¹

Step-3: Factors of 522

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

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

Step-4: Factors of 538

List of positive integer factors of 538 that divides 522 without a remainder.

1, 2, 269

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 522 and 538. The biggest common factor number is the GCF number.
So the greatest common factor 522 and 538 is 2.

Also check out the Least Common Multiple of 522 and 538