Greatest Common Factor of 30 and 36

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 30, 36 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 30 and 36 is 6.

GCF(30,36) = 6

GCF of 30 and 36

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

GCF of:
and

Greatest Common Factor of 30 and 36

GCF of 30 and 36 is 6

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 36


2 36
2 18
3 9
3 3
1

Prime factors of 36 are 2,3. Prime factorization of 36 in exponential form is:

36 = 22×32

∴ So by taking common prime factors GCF of 30 and 36 is 6

Greatest Common Factor of 30 and 36 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 36

List of positive integer factors of 36 that divides 36 without a remainder.

1,2,3,4,6,9,12,18,36

Greatest Common Factor

We found the factors and prime factorization of 30 and 36. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 36 is 6.

Also check out the Least Common Multiple of 30 and 36

Properties of GCF 30 and 36

(i) The GCF of 30 and 36 is associative

GCF of 30 and 36 = GCF of 36 and 30

Related Greatest Common Factor of 30

Related Greatest Common Factor of 36

Frequently Asked Questions on GCF of 30 and 36

1. What is the GCF of 30 and 36?

Answer: GCF of 30 and 36 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 36?

Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.

4. How to Find the GCF of 30 and 36?

Answer:

Greatest Common Factor of 30 and 36 = 6

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 36

36 = 2 x 2 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 30 and 36 is 6