What is the Greatest Common Factor of 546 and 558?

Greatest common factor (GCF) of 546 and 558 is 6.

GCF(546,558) = 6

We will now calculate the prime factors of 546 and 558, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 546 and 558.

How to find the GCF of 546 and 558?

We will first find the prime factorization of 546 and 558. After we will calculate the factors of 546 and 558 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 558

Prime factors of 558 are 2, 3, 31. Prime factorization of 558 in exponential form is:

558 = 2¹ × 3² × 31¹

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 558

List of positive integer factors of 558 that divides 546 without a remainder.

1, 2, 3, 6, 9, 18, 31, 62, 93, 186, 279

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 546 and 558. The biggest common factor number is the GCF number.
So the greatest common factor 546 and 558 is 6.

Also check out the Least Common Multiple of 546 and 558