What is the Greatest Common Factor of 360 and 540?

Greatest common factor (GCF) of 360 and 540 is 180.

GCF(360,540) = 180

We will now calculate the prime factors of 360 and 540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 360 and 540.

How to find the GCF of 360 and 540?

We will first find the prime factorization of 360 and 540. After we will calculate the factors of 360 and 540 and find the biggest common factor number .

Step-1: Prime Factorization of 360

Prime factors of 360 are 2, 3, 5. Prime factorization of 360 in exponential form is:

360 = 2³ × 3² × 5¹

Step-2: 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-3: Factors of 360

List of positive integer factors of 360 that divides 360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180

Step-4: Factors of 540

List of positive integer factors of 540 that divides 360 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 360 and 540. The biggest common factor number is the GCF number.
So the greatest common factor 360 and 540 is 180.

Also check out the Least Common Multiple of 360 and 540