What is the Greatest Common Factor of 264 and 275?

Greatest common factor (GCF) of 264 and 275 is 11.

GCF(264,275) = 11

We will now calculate the prime factors of 264 and 275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 264 and 275.

How to find the GCF of 264 and 275?

We will first find the prime factorization of 264 and 275. After we will calculate the factors of 264 and 275 and find the biggest common factor number .

Step-1: Prime Factorization of 264

Prime factors of 264 are 2, 3, 11. Prime factorization of 264 in exponential form is:

264 = 2³ × 3¹ × 11¹

Step-2: Prime Factorization of 275

Prime factors of 275 are 5, 11. Prime factorization of 275 in exponential form is:

275 = 5² × 11¹

Step-3: Factors of 264

List of positive integer factors of 264 that divides 264 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132

Step-4: Factors of 275

List of positive integer factors of 275 that divides 264 without a remainder.

1, 5, 11, 25, 55

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 264 and 275. The biggest common factor number is the GCF number.
So the greatest common factor 264 and 275 is 11.

Also check out the Least Common Multiple of 264 and 275