Greatest Common Factor of 42 and 56

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, 56 i.e. 14 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 42 and 56 is 14.

GCF(42,56) = 14

GCF of 42 and 56

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

GCF of:
and

Greatest Common Factor of 42 and 56

GCF of 42 and 56 is 14

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 56


2 56
2 28
2 14
7 7
1

Prime factors of 56 are 2,7. Prime factorization of 56 in exponential form is:

56 = 23×71

∴ So by taking common prime factors GCF of 42 and 56 is 14

Greatest Common Factor of 42 and 56 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 56

List of positive integer factors of 56 that divides 56 without a remainder.

1,2,4,7,8,14,28,56

Greatest Common Factor

We found the factors and prime factorization of 42 and 56. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 56 is 14.

Also check out the Least Common Multiple of 42 and 56

Properties of GCF 42 and 56

(i) The GCF of 42 and 56 is associative

GCF of 42 and 56 = GCF of 56 and 42

Related Greatest Common Factor of 42

Related Greatest Common Factor of 56

Frequently Asked Questions on GCF of 42 and 56

1. What is the GCF of 42 and 56?

Answer: GCF of 42 and 56 is 14.

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 56?

Answer: Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. There are 8 integers that are factors of 56. The greatest factor of 56 is 56.

4. How to Find the GCF of 42 and 56?

Answer:

Greatest Common Factor of 42 and 56 = 14

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 56

56 = 2 x 2 x 2 x 7

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

GCF = 2 x 7 = 14

Step 4: Therefore, the greatest common factor of 42 and 56 is 14