What is the Greatest Common Factor of 723 and 728?

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

GCF(723,728) = 1

We will now calculate the prime factors of 723 and 728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 723 and 728.

How to find the GCF of 723 and 728?

We will first find the prime factorization of 723 and 728. After we will calculate the factors of 723 and 728 and find the biggest common factor number .

Step-1: Prime Factorization of 723

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

723 = 3¹ × 241¹

Step-2: Prime Factorization of 728

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

728 = 2³ × 7¹ × 13¹

Step-3: Factors of 723

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

1, 3, 241

Step-4: Factors of 728

List of positive integer factors of 728 that divides 723 without a remainder.

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

Final Step: Biggest Common Factor Number

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