What is the Greatest Common Factor of 256 and 264?

Greatest common factor (GCF) of 256 and 264 is 8.

GCF(256,264) = 8

We will now calculate the prime factors of 256 and 264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 256 and 264.

How to find the GCF of 256 and 264?

We will first find the prime factorization of 256 and 264. After we will calculate the factors of 256 and 264 and find the biggest common factor number .

Step-1: Prime Factorization of 256

Prime factors of 256 are 2. Prime factorization of 256 in exponential form is:

256 = 2⁸

Step-2: 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-3: Factors of 256

List of positive integer factors of 256 that divides 256 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128

Step-4: Factors of 264

List of positive integer factors of 264 that divides 256 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 256 and 264. The biggest common factor number is the GCF number.
So the greatest common factor 256 and 264 is 8.

Also check out the Least Common Multiple of 256 and 264