What is the Greatest Common Factor of 9723 and 9738?

Greatest common factor (GCF) of 9723 and 9738 is 3.

GCF(9723,9738) = 3

We will now calculate the prime factors of 9723 and 9738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9723 and 9738.

How to find the GCF of 9723 and 9738?

We will first find the prime factorization of 9723 and 9738. After we will calculate the factors of 9723 and 9738 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 9738

Prime factors of 9738 are 2, 3, 541. Prime factorization of 9738 in exponential form is:

9738 = 2¹ × 3² × 541¹

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 9738

List of positive integer factors of 9738 that divides 9723 without a remainder.

1, 2, 3, 6, 9, 18, 541, 1082, 1623, 3246, 4869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9723 and 9738. The biggest common factor number is the GCF number.
So the greatest common factor 9723 and 9738 is 3.

Also check out the Least Common Multiple of 9723 and 9738