Greatest Common Factor of 338 and 340

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

Greatest common factor (GCF) of 338 and 340 is 2.

GCF(338,340) = 2

GCF of 338 and 340

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

GCF of:
and

Greatest Common Factor of 338 and 340

GCF of 338 and 340 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 340


2 340
2 170
5 85
17 17
1

Prime factors of 340 are 2,5,17. Prime factorization of 340 in exponential form is:

340 = 22×51×171

∴ So by taking common prime factors GCF of 338 and 340 is 2

Greatest Common Factor of 338 and 340 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 340

List of positive integer factors of 340 that divides 340 without a remainder.

1,2,4,5,10,17,20,34,68,85,170,340

Greatest Common Factor

We found the factors and prime factorization of 338 and 340. The biggest common factor number is the GCF number.
So the greatest common factor 338 and 340 is 2.

Also check out the Least Common Multiple of 338 and 340

Properties of GCF 338 and 340

(i) The GCF of 338 and 340 is associative

GCF of 338 and 340 = GCF of 340 and 338

Related Greatest Common Factor of 338

Related Greatest Common Factor of 340

Frequently Asked Questions on GCF of 338 and 340

1. What is the GCF of 338 and 340?

Answer: GCF of 338 and 340 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 340?

Answer: Factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340. There are 12 integers that are factors of 340. The greatest factor of 340 is 340.

4. How to Find the GCF of 338 and 340?

Answer:

Greatest Common Factor of 338 and 340 = 2

Step 1: Find the prime factorization of 338

338 = 2 x 13 x 13

Step 2: Find the prime factorization of 340

340 = 2 x 2 x 5 x 17

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 340 is 2