What is the Greatest Common Factor of 240 and 285?

Greatest common factor (GCF) of 240 and 285 is 15.

GCF(240,285) = 15

We will now calculate the prime factors of 240 and 285, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 240 and 285.

How to find the GCF of 240 and 285?

We will first find the prime factorization of 240 and 285. After we will calculate the factors of 240 and 285 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 285

Prime factors of 285 are 3, 5, 19. Prime factorization of 285 in exponential form is:

285 = 3¹ × 5¹ × 19¹

Step-3: Factors of 240

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

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

Step-4: Factors of 285

List of positive integer factors of 285 that divides 240 without a remainder.

1, 3, 5, 15, 19, 57, 95

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 240 and 285. The biggest common factor number is the GCF number.
So the greatest common factor 240 and 285 is 15.

Also check out the Least Common Multiple of 240 and 285