Greatest Common Factor of 42 and 54

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 42, 54 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 42 and 54 is 6.

GCF(42,54) = 6

GCF of 42 and 54

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

GCF of:
and

Greatest Common Factor of 42 and 54

GCF of 42 and 54 is 6

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

Prime Factorization of 54


2 54
3 27
3 9
3 3
1

Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:

54 = 21×33

∴ So by taking common prime factors GCF of 42 and 54 is 6

Greatest Common Factor of 42 and 54 by matching factors method

Factors of 42

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

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

Factors of 54

List of positive integer factors of 54 that divides 54 without a remainder.

1,2,3,6,9,18,27,54

Greatest Common Factor

We found the factors and prime factorization of 42 and 54. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 54 is 6.

Also check out the Least Common Multiple of 42 and 54

Properties of GCF 42 and 54

(i) The GCF of 42 and 54 is associative

GCF of 42 and 54 = GCF of 54 and 42

Related Greatest Common Factor of 42

Related Greatest Common Factor of 54

Frequently Asked Questions on GCF of 42 and 54

1. What is the GCF of 42 and 54?

Answer: GCF of 42 and 54 is 6.

2. 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.

3. What are the Factors of 54?

Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.

4. How to Find the GCF of 42 and 54?

Answer:

Greatest Common Factor of 42 and 54 = 6

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 42 and 54 is 6