What is the Greatest Common Factor of 228 and 240?

Greatest common factor (GCF) of 228 and 240 is 12.

GCF(228,240) = 12

We will now calculate the prime factors of 228 and 240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 228 and 240.

How to find the GCF of 228 and 240?

We will first find the prime factorization of 228 and 240. After we will calculate the factors of 228 and 240 and find the biggest common factor number .

Step-1: Prime Factorization of 228

Prime factors of 228 are 2, 3, 19. Prime factorization of 228 in exponential form is:

228 = 2² × 3¹ × 19¹

Step-2: Prime Factorization of 240

Prime factors of 240 are 2, 3, 5. Prime factorization of 240 in exponential form is:

240 = 2⁴ × 3¹ × 5¹

Step-3: Factors of 228

List of positive integer factors of 228 that divides 228 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114

Step-4: Factors of 240

List of positive integer factors of 240 that divides 228 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 228 and 240. The biggest common factor number is the GCF number.
So the greatest common factor 228 and 240 is 12.

Also check out the Least Common Multiple of 228 and 240