What is the Greatest Common Factor of 567 and 582?

Greatest common factor (GCF) of 567 and 582 is 3.

GCF(567,582) = 3

We will now calculate the prime factors of 567 and 582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 567 and 582.

How to find the GCF of 567 and 582?

We will first find the prime factorization of 567 and 582. After we will calculate the factors of 567 and 582 and find the biggest common factor number .

Step-1: Prime Factorization of 567

Prime factors of 567 are 3, 7. Prime factorization of 567 in exponential form is:

567 = 3⁴ × 7¹

Step-2: Prime Factorization of 582

Prime factors of 582 are 2, 3, 97. Prime factorization of 582 in exponential form is:

582 = 2¹ × 3¹ × 97¹

Step-3: Factors of 567

List of positive integer factors of 567 that divides 567 without a remainder.

1, 3, 7, 9, 21, 27, 63, 81, 189

Step-4: Factors of 582

List of positive integer factors of 582 that divides 567 without a remainder.

1, 2, 3, 6, 97, 194, 291

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 567 and 582. The biggest common factor number is the GCF number.
So the greatest common factor 567 and 582 is 3.

Also check out the Least Common Multiple of 567 and 582