Greatest Common Factor of 54 and 63

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, 63 i.e. 9 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 54 and 63 is 9.

GCF(54,63) = 9

GCF of 54 and 63

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

GCF of:
and

Greatest Common Factor of 54 and 63

GCF of 54 and 63 is 9

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 63


3 63
3 21
7 7
1

Prime factors of 63 are 3,7. Prime factorization of 63 in exponential form is:

63 = 32×71

∴ So by taking common prime factors GCF of 54 and 63 is 9

Greatest Common Factor of 54 and 63 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 63

List of positive integer factors of 63 that divides 63 without a remainder.

1,3,7,9,21,63

Greatest Common Factor

We found the factors and prime factorization of 54 and 63. The biggest common factor number is the GCF number.
So the greatest common factor 54 and 63 is 9.

Also check out the Least Common Multiple of 54 and 63

Properties of GCF 54 and 63

(i) The GCF of 54 and 63 is associative

GCF of 54 and 63 = GCF of 63 and 54

Related Greatest Common Factor of 54

Related Greatest Common Factor of 63

Frequently Asked Questions on GCF of 54 and 63

1. What is the GCF of 54 and 63?

Answer: GCF of 54 and 63 is 9.

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 63?

Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.

4. How to Find the GCF of 54 and 63?

Answer:

Greatest Common Factor of 54 and 63 = 9

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 63

63 = 3 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 = 3 x 3 = 9

Step 4: Therefore, the greatest common factor of 54 and 63 is 9