What is the Greatest Common Factor of 546 and 561?

Greatest common factor (GCF) of 546 and 561 is 3.

GCF(546,561) = 3

We will now calculate the prime factors of 546 and 561, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 546 and 561.

How to find the GCF of 546 and 561?

We will first find the prime factorization of 546 and 561. After we will calculate the factors of 546 and 561 and find the biggest common factor number .

Step-1: Prime Factorization of 546

Prime factors of 546 are 2, 3, 7, 13. Prime factorization of 546 in exponential form is:

546 = 2¹ × 3¹ × 7¹ × 13¹

Step-2: 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-3: Factors of 546

List of positive integer factors of 546 that divides 546 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273

Step-4: Factors of 561

List of positive integer factors of 561 that divides 546 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 546 and 561. The biggest common factor number is the GCF number.
So the greatest common factor 546 and 561 is 3.

Also check out the Least Common Multiple of 546 and 561