What is the Greatest Common Factor of 546 and 559?

Greatest common factor (GCF) of 546 and 559 is 13.

GCF(546,559) = 13

We will now calculate the prime factors of 546 and 559, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 546 and 559.

How to find the GCF of 546 and 559?

We will first find the prime factorization of 546 and 559. After we will calculate the factors of 546 and 559 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 559

Prime factors of 559 are 13, 43. Prime factorization of 559 in exponential form is:

559 = 13¹ × 43¹

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 559

List of positive integer factors of 559 that divides 546 without a remainder.

1, 13, 43

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 546 and 559. The biggest common factor number is the GCF number.
So the greatest common factor 546 and 559 is 13.

Also check out the Least Common Multiple of 546 and 559