What is the Greatest Common Factor of 9723 and 9729?

Greatest common factor (GCF) of 9723 and 9729 is 3.

GCF(9723,9729) = 3

We will now calculate the prime factors of 9723 and 9729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9723 and 9729.

How to find the GCF of 9723 and 9729?

We will first find the prime factorization of 9723 and 9729. After we will calculate the factors of 9723 and 9729 and find the biggest common factor number .

Step-1: Prime Factorization of 9723

Prime factors of 9723 are 3, 7, 463. Prime factorization of 9723 in exponential form is:

9723 = 3¹ × 7¹ × 463¹

Step-2: Prime Factorization of 9729

Prime factors of 9729 are 3, 23, 47. Prime factorization of 9729 in exponential form is:

9729 = 3² × 23¹ × 47¹

Step-3: Factors of 9723

List of positive integer factors of 9723 that divides 9723 without a remainder.

1, 3, 7, 21, 463, 1389, 3241

Step-4: Factors of 9729

List of positive integer factors of 9729 that divides 9723 without a remainder.

1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9723 and 9729. The biggest common factor number is the GCF number.
So the greatest common factor 9723 and 9729 is 3.

Also check out the Least Common Multiple of 9723 and 9729