Greatest Common Factor of 42 and 28

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

Greatest common factor (GCF) of 42 and 28 is 14.

GCF(42,28) = 14

GCF of 42 and 28

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

GCF of:
and

Greatest Common Factor of 42 and 28

GCF of 42 and 28 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 28


2 28
2 14
7 7
1

Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:

28 = 22×71

∴ So by taking common prime factors GCF of 42 and 28 is 14

Greatest Common Factor of 42 and 28 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 28

List of positive integer factors of 28 that divides 28 without a remainder.

1,2,4,7,14,28

Greatest Common Factor

We found the factors and prime factorization of 42 and 28. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 28 is 14.

Also check out the Least Common Multiple of 42 and 28

Properties of GCF 42 and 28

(i) The GCF of 42 and 28 is associative

GCF of 42 and 28 = GCF of 28 and 42

Related Greatest Common Factor of 42

Related Greatest Common Factor of 28

Frequently Asked Questions on GCF of 42 and 28

1. What is the GCF of 42 and 28?

Answer: GCF of 42 and 28 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 28?

Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.

4. How to Find the GCF of 42 and 28?

Answer:

Greatest Common Factor of 42 and 28 = 14

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 28

28 = 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 28 is 14