Greatest Common Factor of 36 and 54

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 36, 54 i.e. 18 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 36 and 54 is 18.

GCF(36,54) = 18

GCF of 36 and 54

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

GCF of:
and

Greatest Common Factor of 36 and 54

GCF of 36 and 54 is 18

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

Prime Factorization of 54


2 54
3 27
3 9
3 3
1

Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:

54 = 21×33

∴ So by taking common prime factors GCF of 36 and 54 is 18

Greatest Common Factor of 36 and 54 by matching factors method

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

Factors of 54

List of positive integer factors of 54 that divides 54 without a remainder.

1,2,3,6,9,18,27,54

Greatest Common Factor

We found the factors and prime factorization of 36 and 54. The biggest common factor number is the GCF number.
So the greatest common factor 36 and 54 is 18.

Also check out the Least Common Multiple of 36 and 54

Properties of GCF 36 and 54

(i) The GCF of 36 and 54 is associative

GCF of 36 and 54 = GCF of 54 and 36

Related Greatest Common Factor of 36

Related Greatest Common Factor of 54

Frequently Asked Questions on GCF of 36 and 54

1. What is the GCF of 36 and 54?

Answer: GCF of 36 and 54 is 18.

2. 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.

3. What are the Factors of 54?

Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.

4. How to Find the GCF of 36 and 54?

Answer:

Greatest Common Factor of 36 and 54 = 18

Step 1: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 54

54 = 2 x 3 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 x 3 = 18

Step 4: Therefore, the greatest common factor of 36 and 54 is 18