Greatest Common Factor of 54 and 72

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 54, 72 i.e. 18 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 54 and 72 is 18.

GCF(54,72) = 18

GCF of 54 and 72

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

GCF of:
and

Greatest Common Factor of 54 and 72

GCF of 54 and 72 is 18

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

Prime Factorization of 72


2 72
2 36
2 18
3 9
3 3
1

Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:

72 = 23×32

∴ So by taking common prime factors GCF of 54 and 72 is 18

Greatest Common Factor of 54 and 72 by matching factors method

Factors of 54

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

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

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

Greatest Common Factor

We found the factors and prime factorization of 54 and 72. The biggest common factor number is the GCF number.
So the greatest common factor 54 and 72 is 18.

Also check out the Least Common Multiple of 54 and 72

Properties of GCF 54 and 72

(i) The GCF of 54 and 72 is associative

GCF of 54 and 72 = GCF of 72 and 54

Related Greatest Common Factor of 54

Related Greatest Common Factor of 72

Frequently Asked Questions on GCF of 54 and 72

1. What is the GCF of 54 and 72?

Answer: GCF of 54 and 72 is 18.

2. 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.

3. What are the Factors of 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

4. How to Find the GCF of 54 and 72?

Answer:

Greatest Common Factor of 54 and 72 = 18

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 72

72 = 2 x 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 x 3 = 18

Step 4: Therefore, the greatest common factor of 54 and 72 is 18