Greatest Common Factor of 723 and 728

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, 728 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 723 and 728 is 1.

GCF(723,728) = 1

GCF of 723 and 728

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

GCF of:
and

Greatest Common Factor of 723 and 728

GCF of 723 and 728 is 1

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 728


2 728
2 364
2 182
7 91
13 13
1

Prime factors of 728 are 2,7,13. Prime factorization of 728 in exponential form is:

728 = 23×71×131

∴ So by taking common prime factors GCF of 723 and 728 is 1

Greatest Common Factor of 723 and 728 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 728

List of positive integer factors of 728 that divides 728 without a remainder.

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Greatest Common Factor

We found the factors and prime factorization of 723 and 728. The biggest common factor number is the GCF number.
So the greatest common factor 723 and 728 is 1.

Also check out the Least Common Multiple of 723 and 728

Properties of GCF 723 and 728

(i) The GCF of 723 and 728 is associative

GCF of 723 and 728 = GCF of 728 and 723

Related Greatest Common Factor of 723

Related Greatest Common Factor of 728

Frequently Asked Questions on GCF of 723 and 728

1. What is the GCF of 723 and 728?

Answer: GCF of 723 and 728 is 1.

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 728?

Answer: Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. There are 16 integers that are factors of 728. The greatest factor of 728 is 728.

4. How to Find the GCF of 723 and 728?

Answer:

Greatest Common Factor of 723 and 728 = 1

Step 1: Find the prime factorization of 723

723 = 3 x 241

Step 2: Find the prime factorization of 728

728 = 2 x 2 x 2 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 = = 1

Step 4: Therefore, the greatest common factor of 723 and 728 is 1