What is the Greatest Common Factor of 225 and 240?

Greatest common factor (GCF) of 225 and 240 is 15.

GCF(225,240) = 15

We will now calculate the prime factors of 225 and 240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 225 and 240.

How to find the GCF of 225 and 240?

We will first find the prime factorization of 225 and 240. After we will calculate the factors of 225 and 240 and find the biggest common factor number .

Step-1: Prime Factorization of 225

Prime factors of 225 are 3, 5. Prime factorization of 225 in exponential form is:

225 = 3² × 5²

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 225

List of positive integer factors of 225 that divides 225 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75

Step-4: Factors of 240

List of positive integer factors of 240 that divides 225 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 225 and 240. The biggest common factor number is the GCF number.
So the greatest common factor 225 and 240 is 15.

Also check out the Least Common Multiple of 225 and 240