Greatest Common Factor of 34 and 42

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

Greatest common factor (GCF) of 34 and 42 is 2.

GCF(34,42) = 2

GCF of 34 and 42

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

GCF of:
and

Greatest Common Factor of 34 and 42

GCF of 34 and 42 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 42


2 42
3 21
7 7
1

Prime factors of 42 are 2,3,7. Prime factorization of 42 in exponential form is:

42 = 21×31×71

∴ So by taking common prime factors GCF of 34 and 42 is 2

Greatest Common Factor of 34 and 42 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 42

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

Greatest Common Factor

We found the factors and prime factorization of 34 and 42. The biggest common factor number is the GCF number.
So the greatest common factor 34 and 42 is 2.

Also check out the Least Common Multiple of 34 and 42

Properties of GCF 34 and 42

(i) The GCF of 34 and 42 is associative

GCF of 34 and 42 = GCF of 42 and 34

Related Greatest Common Factor of 34

Related Greatest Common Factor of 42

Frequently Asked Questions on GCF of 34 and 42

1. What is the GCF of 34 and 42?

Answer: GCF of 34 and 42 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 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

4. How to Find the GCF of 34 and 42?

Answer:

Greatest Common Factor of 34 and 42 = 2

Step 1: Find the prime factorization of 34

34 = 2 x 17

Step 2: Find the prime factorization of 42

42 = 2 x 3 x 7

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 42 is 2