What is the Greatest Common Factor of 2700 and 3240?

Greatest common factor (GCF) of 2700 and 3240 is 540.

GCF(2700,3240) = 540

We will now calculate the prime factors of 2700 and 3240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2700 and 3240.

How to find the GCF of 2700 and 3240?

We will first find the prime factorization of 2700 and 3240. After we will calculate the factors of 2700 and 3240 and find the biggest common factor number .

Step-1: Prime Factorization of 2700

Prime factors of 2700 are 2, 3, 5. Prime factorization of 2700 in exponential form is:

2700 = 2² × 3³ × 5²

Step-2: Prime Factorization of 3240

Prime factors of 3240 are 2, 3, 5. Prime factorization of 3240 in exponential form is:

3240 = 2³ × 3⁴ × 5¹

Step-3: Factors of 2700

List of positive integer factors of 2700 that divides 2700 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350

Step-4: Factors of 3240

List of positive integer factors of 3240 that divides 2700 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2700 and 3240. The biggest common factor number is the GCF number.
So the greatest common factor 2700 and 3240 is 540.

Also check out the Least Common Multiple of 2700 and 3240