What is the Greatest Common Factor of 723 and 741?

Greatest common factor (GCF) of 723 and 741 is 3.

GCF(723,741) = 3

We will now calculate the prime factors of 723 and 741, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 723 and 741.

How to find the GCF of 723 and 741?

We will first find the prime factorization of 723 and 741. After we will calculate the factors of 723 and 741 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 741

Prime factors of 741 are 3, 13, 19. Prime factorization of 741 in exponential form is:

741 = 3¹ × 13¹ × 19¹

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 741

List of positive integer factors of 741 that divides 723 without a remainder.

1, 3, 13, 19, 39, 57, 247

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 723 and 741. The biggest common factor number is the GCF number.
So the greatest common factor 723 and 741 is 3.

Also check out the Least Common Multiple of 723 and 741