Greatest Common Factor of 34 and 38

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 34, 38 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 34 and 38 is 2.

GCF(34,38) = 2

GCF of 34 and 38

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

GCF of:
and

Greatest Common Factor of 34 and 38

GCF of 34 and 38 is 2

Prime Factorization of 34


2 34
17 17
1

Prime factors of 34 are 2,17. Prime factorization of 34 in exponential form is:

34 = 21×171

Prime Factorization of 38


2 38
19 19
1

Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:

38 = 21×191

∴ So by taking common prime factors GCF of 34 and 38 is 2

Greatest Common Factor of 34 and 38 by matching factors method

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1,2,19,38

Greatest Common Factor

We found the factors and prime factorization of 34 and 38. The biggest common factor number is the GCF number.
So the greatest common factor 34 and 38 is 2.

Also check out the Least Common Multiple of 34 and 38

Properties of GCF 34 and 38

(i) The GCF of 34 and 38 is associative

GCF of 34 and 38 = GCF of 38 and 34

Related Greatest Common Factor of 34

Related Greatest Common Factor of 38

Frequently Asked Questions on GCF of 34 and 38

1. What is the GCF of 34 and 38?

Answer: GCF of 34 and 38 is 2.

2. What are the Factors of 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

3. What are the Factors of 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

4. How to Find the GCF of 34 and 38?

Answer:

Greatest Common Factor of 34 and 38 = 2

Step 1: Find the prime factorization of 34

34 = 2 x 17

Step 2: Find the prime factorization of 38

38 = 2 x 19

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 34 and 38 is 2