Greatest Common Factor of 338 and 344

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 338, 344 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 338 and 344 is 2.

GCF(338,344) = 2

GCF of 338 and 344

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

GCF of:
and

Greatest Common Factor of 338 and 344

GCF of 338 and 344 is 2

Prime Factorization of 338


2 338
13 169
13 13
1

Prime factors of 338 are 2,13. Prime factorization of 338 in exponential form is:

338 = 21×132

Prime Factorization of 344


2 344
2 172
2 86
43 43
1

Prime factors of 344 are 2,43. Prime factorization of 344 in exponential form is:

344 = 23×431

∴ So by taking common prime factors GCF of 338 and 344 is 2

Greatest Common Factor of 338 and 344 by matching factors method

Factors of 338

List of positive integer factors of 338 that divides 338 without a remainder.

1,2,13,26,169,338

Factors of 344

List of positive integer factors of 344 that divides 344 without a remainder.

1,2,4,8,43,86,172,344

Greatest Common Factor

We found the factors and prime factorization of 338 and 344. The biggest common factor number is the GCF number.
So the greatest common factor 338 and 344 is 2.

Also check out the Least Common Multiple of 338 and 344

Properties of GCF 338 and 344

(i) The GCF of 338 and 344 is associative

GCF of 338 and 344 = GCF of 344 and 338

Related Greatest Common Factor of 338

Related Greatest Common Factor of 344

Frequently Asked Questions on GCF of 338 and 344

1. What is the GCF of 338 and 344?

Answer: GCF of 338 and 344 is 2.

2. What are the Factors of 338?

Answer: Factors of 338 are 1, 2, 13, 26, 169, 338. There are 6 integers that are factors of 338. The greatest factor of 338 is 338.

3. What are the Factors of 344?

Answer: Factors of 344 are 1, 2, 4, 8, 43, 86, 172, 344. There are 8 integers that are factors of 344. The greatest factor of 344 is 344.

4. How to Find the GCF of 338 and 344?

Answer:

Greatest Common Factor of 338 and 344 = 2

Step 1: Find the prime factorization of 338

338 = 2 x 13 x 13

Step 2: Find the prime factorization of 344

344 = 2 x 2 x 2 x 43

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 338 and 344 is 2