Greatest Common Factor of 540 and 546

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 540, 546 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 540 and 546 is 6.

GCF(540,546) = 6

GCF of 540 and 546

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

GCF of:
and

Greatest Common Factor of 540 and 546

GCF of 540 and 546 is 6

Prime Factorization of 540


2 540
2 270
3 135
3 45
3 15
5 5
1

Prime factors of 540 are 2,3,5. Prime factorization of 540 in exponential form is:

540 = 22×33×51

Prime Factorization of 546


2 546
3 273
7 91
13 13
1

Prime factors of 546 are 2,3,7,13. Prime factorization of 546 in exponential form is:

546 = 21×31×71×131

∴ So by taking common prime factors GCF of 540 and 546 is 6

Greatest Common Factor of 540 and 546 by matching factors method

Factors of 540

List of positive integer factors of 540 that divides 540 without a remainder.

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Factors of 546

List of positive integer factors of 546 that divides 546 without a remainder.

1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546

Greatest Common Factor

We found the factors and prime factorization of 540 and 546. The biggest common factor number is the GCF number.
So the greatest common factor 540 and 546 is 6.

Also check out the Least Common Multiple of 540 and 546

Properties of GCF 540 and 546

(i) The GCF of 540 and 546 is associative

GCF of 540 and 546 = GCF of 546 and 540

Related Greatest Common Factor of 540

Related Greatest Common Factor of 546

Frequently Asked Questions on GCF of 540 and 546

1. What is the GCF of 540 and 546?

Answer: GCF of 540 and 546 is 6.

2. What are the Factors of 540?

Answer: Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540. There are 24 integers that are factors of 540. The greatest factor of 540 is 540.

3. What are the Factors of 546?

Answer: Factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546. There are 16 integers that are factors of 546. The greatest factor of 546 is 546.

4. How to Find the GCF of 540 and 546?

Answer:

Greatest Common Factor of 540 and 546 = 6

Step 1: Find the prime factorization of 540

540 = 2 x 2 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 546

546 = 2 x 3 x 7 x 13

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 540 and 546 is 6