What is the Greatest Common Factor of 270 and 288?

Greatest common factor (GCF) of 270 and 288 is 18.

GCF(270,288) = 18

We will now calculate the prime factors of 270 and 288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 270 and 288.

How to find the GCF of 270 and 288?

We will first find the prime factorization of 270 and 288. After we will calculate the factors of 270 and 288 and find the biggest common factor number .

Step-1: Prime Factorization of 270

Prime factors of 270 are 2, 3, 5. Prime factorization of 270 in exponential form is:

270 = 2¹ × 3³ × 5¹

Step-2: Prime Factorization of 288

Prime factors of 288 are 2, 3. Prime factorization of 288 in exponential form is:

288 = 2⁵ × 3²

Step-3: Factors of 270

List of positive integer factors of 270 that divides 270 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135

Step-4: Factors of 288

List of positive integer factors of 288 that divides 270 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 270 and 288. The biggest common factor number is the GCF number.
So the greatest common factor 270 and 288 is 18.

Also check out the Least Common Multiple of 270 and 288