Greatest Common Factor of 256 and 262

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, 262 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 256 and 262 is 2.

GCF(256,262) = 2

GCF of 256 and 262

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

GCF of:
and

Greatest Common Factor of 256 and 262

GCF of 256 and 262 is 2

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 262


2 262
131 131
1

Prime factors of 262 are 2.Prime factorization of 262 in exponential form is:

262 = 21×1311

∴ So by taking common prime factors GCF of 256 and 262 is 2

Greatest Common Factor of 256 and 262 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 262

List of positive integer factors of 262 that divides 262 without a remainder.

1,2,131,262

Greatest Common Factor

We found the factors and prime factorization of 256 and 262. The biggest common factor number is the GCF number.
So the greatest common factor 256 and 262 is 2.

Also check out the Least Common Multiple of 256 and 262

Properties of GCF 256 and 262

(i) The GCF of 256 and 262 is associative

GCF of 256 and 262 = GCF of 262 and 256

Related Greatest Common Factor of 256

Related Greatest Common Factor of 262

Frequently Asked Questions on GCF of 256 and 262

1. What is the GCF of 256 and 262?

Answer: GCF of 256 and 262 is 2.

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 262?

Answer: Factors of 262 are 1, 2, 131, 262. There are 4 integers that are factors of 262. The greatest factor of 262 is 262.

4. How to Find the GCF of 256 and 262?

Answer:

Greatest Common Factor of 256 and 262 = 2

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 262

262 = 2 x 131

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

GCF = 2

Step 4: Therefore, the greatest common factor of 256 and 262 is 2