Greatest Common Factor of 723 and 729

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 723, 729 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 723 and 729 is 3.

GCF(723,729) = 3

GCF of 723 and 729

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

GCF of:
and

Greatest Common Factor of 723 and 729

GCF of 723 and 729 is 3

Prime Factorization of 723


3 723
241 241
1

Prime factors of 723 are 3,241. Prime factorization of 723 in exponential form is:

723 = 31×2411

Prime Factorization of 729


3 729
3 243
3 81
3 27
3 9
3 3
1

Prime factors of 729 are 3. Prime factorization of 729 in exponential form is:

729 = 36

∴ So by taking common prime factors GCF of 723 and 729 is 3

Greatest Common Factor of 723 and 729 by matching factors method

Factors of 723

List of positive integer factors of 723 that divides 723 without a remainder.

1,3,241,723

Factors of 729

List of positive integer factors of 729 that divides 729 without a remainder.

1,3,9,27,81,243,729

Greatest Common Factor

We found the factors and prime factorization of 723 and 729. The biggest common factor number is the GCF number.
So the greatest common factor 723 and 729 is 3.

Also check out the Least Common Multiple of 723 and 729

Properties of GCF 723 and 729

(i) The GCF of 723 and 729 is associative

GCF of 723 and 729 = GCF of 729 and 723

Related Greatest Common Factor of 723

Related Greatest Common Factor of 729

Frequently Asked Questions on GCF of 723 and 729

1. What is the GCF of 723 and 729?

Answer: GCF of 723 and 729 is 3.

2. What are the Factors of 723?

Answer: Factors of 723 are 1, 3, 241, 723. There are 4 integers that are factors of 723. The greatest factor of 723 is 723.

3. What are the Factors of 729?

Answer: Factors of 729 are 1, 3, 9, 27, 81, 243, 729. There are 7 integers that are factors of 729. The greatest factor of 729 is 729.

4. How to Find the GCF of 723 and 729?

Answer:

Greatest Common Factor of 723 and 729 = 3

Step 1: Find the prime factorization of 723

723 = 3 x 241

Step 2: Find the prime factorization of 729

729 = 3 x 3 x 3 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 = 3

Step 4: Therefore, the greatest common factor of 723 and 729 is 3