# Greatest Common Factor of 30 and 42

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 30, 42 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 30 and 42 is 6.

GCF(30,42) = 6

## GCF of 30 and 42

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

GCF of:
and

### Greatest Common Factor of 30 and 42 by Prime factorization method

Prime Factorization of 30

 2 30 3 15 5 5 1

Prime factors of 30 are 2,3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

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 30 and 42 is 6

### Greatest Common Factor of 30 and 42 by matching factors method

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

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 30 and 42. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 42 is 6.

Also check out the Least Common Multiple of 30 and 42

### Properties of GCF 30 and 42

(i) The GCF of 30 and 42 is associative

GCF of 30 and 42 = GCF of 42 and 30

### Frequently Asked Questions on GCF of 30 and 42

1. What is the GCF of 30 and 42?

Answer: GCF of 30 and 42 is 6.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

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 30 and 42?

Greatest Common Factor of 30 and 42 = 6

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

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 x 3 = 6

Step 4: Therefore, the greatest common factor of 30 and 42 is 6