What is the Greatest Common Factor of 540 and 549?

Greatest common factor (GCF) of 540 and 549 is 9.

GCF(540,549) = 9

We will now calculate the prime factors of 540 and 549, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 540 and 549.

How to find the GCF of 540 and 549?

We will first find the prime factorization of 540 and 549. After we will calculate the factors of 540 and 549 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 549

Prime factors of 549 are 3, 61. Prime factorization of 549 in exponential form is:

549 = 3² × 61¹

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 549

List of positive integer factors of 549 that divides 540 without a remainder.

1, 3, 9, 61, 183

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 540 and 549. The biggest common factor number is the GCF number.
So the greatest common factor 540 and 549 is 9.

Also check out the Least Common Multiple of 540 and 549