Greatest Common Factor of 259 and 266

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 259, 266 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 259 and 266 is 7.

GCF(259,266) = 7

GCF of 259 and 266

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

GCF of:
and

Greatest Common Factor of 259 and 266

GCF of 259 and 266 is 7

Prime Factorization of 259


7 259
37 37
1

Prime factors of 259 are 7,37. Prime factorization of 259 in exponential form is:

259 = 71×371

Prime Factorization of 266


2 266
7 133
19 19
1

Prime factors of 266 are 2,7,19. Prime factorization of 266 in exponential form is:

266 = 21×71×191

∴ So by taking common prime factors GCF of 259 and 266 is 7

Greatest Common Factor of 259 and 266 by matching factors method

Factors of 259

List of positive integer factors of 259 that divides 259 without a remainder.

1,7,37,259

Factors of 266

List of positive integer factors of 266 that divides 266 without a remainder.

1,2,7,14,19,38,133,266

Greatest Common Factor

We found the factors and prime factorization of 259 and 266. The biggest common factor number is the GCF number.
So the greatest common factor 259 and 266 is 7.

Also check out the Least Common Multiple of 259 and 266

Properties of GCF 259 and 266

(i) The GCF of 259 and 266 is associative

GCF of 259 and 266 = GCF of 266 and 259

Related Greatest Common Factor of 259

Related Greatest Common Factor of 266

Frequently Asked Questions on GCF of 259 and 266

1. What is the GCF of 259 and 266?

Answer: GCF of 259 and 266 is 7.

2. What are the Factors of 259?

Answer: Factors of 259 are 1, 7, 37, 259. There are 4 integers that are factors of 259. The greatest factor of 259 is 259.

3. What are the Factors of 266?

Answer: Factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266. There are 8 integers that are factors of 266. The greatest factor of 266 is 266.

4. How to Find the GCF of 259 and 266?

Answer:

Greatest Common Factor of 259 and 266 = 7

Step 1: Find the prime factorization of 259

259 = 7 x 37

Step 2: Find the prime factorization of 266

266 = 2 x 7 x 19

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

GCF = 7

Step 4: Therefore, the greatest common factor of 259 and 266 is 7