What is the Greatest Common Factor of 561 and 567?

Greatest common factor (GCF) of 561 and 567 is 3.

GCF(561,567) = 3

We will now calculate the prime factors of 561 and 567, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 561 and 567.

How to find the GCF of 561 and 567?

We will first find the prime factorization of 561 and 567. After we will calculate the factors of 561 and 567 and find the biggest common factor number .

Step-1: Prime Factorization of 561

Prime factors of 561 are 3, 11, 17. Prime factorization of 561 in exponential form is:

561 = 3¹ × 11¹ × 17¹

Step-2: Prime Factorization of 567

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

567 = 3⁴ × 7¹

Step-3: Factors of 561

List of positive integer factors of 561 that divides 561 without a remainder.

1, 3, 11, 17, 33, 51, 187

Step-4: Factors of 567

List of positive integer factors of 567 that divides 561 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 561 and 567. The biggest common factor number is the GCF number.
So the greatest common factor 561 and 567 is 3.

Also check out the Least Common Multiple of 561 and 567