What is the Greatest Common Factor of 540 and 546?

Greatest common factor (GCF) of 540 and 546 is 6.

GCF(540,546) = 6

We will now calculate the prime factors of 540 and 546, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 540 and 546.

How to find the GCF of 540 and 546?

We will first find the prime factorization of 540 and 546. After we will calculate the factors of 540 and 546 and find the biggest common factor number .

Step-1: Prime Factorization of 540

Prime factors of 540 are 2, 3, 5. Prime factorization of 540 in exponential form is:

540 = 2² × 3³ × 5¹

Step-2: 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-3: Factors of 540

List of positive integer factors of 540 that divides 540 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270

Step-4: Factors of 546

List of positive integer factors of 546 that divides 540 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 540 and 546. The biggest common factor number is the GCF number.
So the greatest common factor 540 and 546 is 6.

Also check out the Least Common Multiple of 540 and 546