What is the Greatest Common Factor of 546 and 564?

Greatest common factor (GCF) of 546 and 564 is 6.

GCF(546,564) = 6

We will now calculate the prime factors of 546 and 564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 546 and 564.

How to find the GCF of 546 and 564?

We will first find the prime factorization of 546 and 564. After we will calculate the factors of 546 and 564 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 564

Prime factors of 564 are 2, 3, 47. Prime factorization of 564 in exponential form is:

564 = 2² × 3¹ × 47¹

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 564

List of positive integer factors of 564 that divides 546 without a remainder.

1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 546 and 564. The biggest common factor number is the GCF number.
So the greatest common factor 546 and 564 is 6.

Also check out the Least Common Multiple of 546 and 564