Greatest Common Factor of 38 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 38, 42 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 38 and 42 is 2.

GCF(38,42) = 2

GCF of 38 and 42

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

GCF of:
and

Greatest Common Factor of 38 and 42

GCF of 38 and 42 is 2

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

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 38 and 42 is 2

Greatest Common Factor of 38 and 42 by matching factors method

Factors of 38

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

1,2,19,38

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 38 and 42. The biggest common factor number is the GCF number.
So the greatest common factor 38 and 42 is 2.

Also check out the Least Common Multiple of 38 and 42

Properties of GCF 38 and 42

(i) The GCF of 38 and 42 is associative

GCF of 38 and 42 = GCF of 42 and 38

Related Greatest Common Factor of 38

Related Greatest Common Factor of 42

Frequently Asked Questions on GCF of 38 and 42

1. What is the GCF of 38 and 42?

Answer: GCF of 38 and 42 is 2.

2. 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.

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 38 and 42?

Answer:

Greatest Common Factor of 38 and 42 = 2

Step 1: Find the prime factorization of 38

38 = 2 x 19

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 38 and 42 is 2