What is the Greatest Common Factor of 240 and 252?

Greatest common factor (GCF) of 240 and 252 is 12.

GCF(240,252) = 12

We will now calculate the prime factors of 240 and 252, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 240 and 252.

How to find the GCF of 240 and 252?

We will first find the prime factorization of 240 and 252. After we will calculate the factors of 240 and 252 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 252

Prime factors of 252 are 2, 3, 7. Prime factorization of 252 in exponential form is:

252 = 2² × 3² × 7¹

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 252

List of positive integer factors of 252 that divides 240 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 240 and 252. The biggest common factor number is the GCF number.
So the greatest common factor 240 and 252 is 12.

Also check out the Least Common Multiple of 240 and 252