What is the Greatest Common Factor of 567 and 585?

Greatest common factor (GCF) of 567 and 585 is 9.

GCF(567,585) = 9

We will now calculate the prime factors of 567 and 585, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 567 and 585.

How to find the GCF of 567 and 585?

We will first find the prime factorization of 567 and 585. After we will calculate the factors of 567 and 585 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 585

Prime factors of 585 are 3, 5, 13. Prime factorization of 585 in exponential form is:

585 = 3² × 5¹ × 13¹

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 585

List of positive integer factors of 585 that divides 567 without a remainder.

1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 567 and 585. The biggest common factor number is the GCF number.
So the greatest common factor 567 and 585 is 9.

Also check out the Least Common Multiple of 567 and 585