Greatest Common Factor of 42 and 60

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

Greatest common factor (GCF) of 42 and 60 is 6.

GCF(42,60) = 6

GCF of 42 and 60

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

GCF of:
and

Greatest Common Factor of 42 and 60

GCF of 42 and 60 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 60


2 60
2 30
3 15
5 5
1

Prime factors of 60 are 2,3,5. Prime factorization of 60 in exponential form is:

60 = 22×31×51

∴ So by taking common prime factors GCF of 42 and 60 is 6

Greatest Common Factor of 42 and 60 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 60

List of positive integer factors of 60 that divides 60 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60

Greatest Common Factor

We found the factors and prime factorization of 42 and 60. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 60 is 6.

Also check out the Least Common Multiple of 42 and 60

Properties of GCF 42 and 60

(i) The GCF of 42 and 60 is associative

GCF of 42 and 60 = GCF of 60 and 42

Related Greatest Common Factor of 42

Related Greatest Common Factor of 60

Frequently Asked Questions on GCF of 42 and 60

1. What is the GCF of 42 and 60?

Answer: GCF of 42 and 60 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 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

4. How to Find the GCF of 42 and 60?

Answer:

Greatest Common Factor of 42 and 60 = 6

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

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 60 is 6