Greatest Common Factor of 256 and 264

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 256, 264 i.e. 8 largest integer by which both the numbers can be divided.

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

GCF(256,264) = 8

GCF of 256 and 264

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 256 and 264

GCF of 256 and 264 is 8

Prime Factorization of 256


2 256
2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

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

256 = 28

Prime Factorization of 264


2 264
2 132
2 66
3 33
11 11
1

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

264 = 23×31×111

∴ So by taking common prime factors GCF of 256 and 264 is 8

Greatest Common Factor of 256 and 264 by matching factors method

Factors of 256

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

1,2,4,8,16,32,64,128,256

Factors of 264

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

1,2,3,4,6,8,11,12,22,24,33,44,66,88,132,264

Greatest Common Factor

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

Properties of GCF 256 and 264

(i) The GCF of 256 and 264 is associative

GCF of 256 and 264 = GCF of 264 and 256

Related Greatest Common Factor of 256

Related Greatest Common Factor of 264

Frequently Asked Questions on GCF of 256 and 264

1. What is the GCF of 256 and 264?

Answer: GCF of 256 and 264 is 8.

2. What are the Factors of 256?

Answer: Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256. There are 9 integers that are factors of 256. The greatest factor of 256 is 256.

3. What are the Factors of 264?

Answer: Factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. There are 16 integers that are factors of 264. The greatest factor of 264 is 264.

4. How to Find the GCF of 256 and 264?

Answer:

Greatest Common Factor of 256 and 264 = 8

Step 1: Find the prime factorization of 256

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 264

264 = 2 x 2 x 2 x 3 x 11

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 256 and 264 is 8