What is the Greatest Common Factor of 9708 and 9723?

Greatest common factor (GCF) of 9708 and 9723 is 3.

GCF(9708,9723) = 3

We will now calculate the prime factors of 9708 and 9723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9708 and 9723.

How to find the GCF of 9708 and 9723?

We will first find the prime factorization of 9708 and 9723. After we will calculate the factors of 9708 and 9723 and find the biggest common factor number .

Step-1: Prime Factorization of 9708

Prime factors of 9708 are 2, 3, 809. Prime factorization of 9708 in exponential form is:

9708 = 2² × 3¹ × 809¹

Step-2: 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-3: Factors of 9708

List of positive integer factors of 9708 that divides 9708 without a remainder.

1, 2, 3, 4, 6, 12, 809, 1618, 2427, 3236, 4854

Step-4: Factors of 9723

List of positive integer factors of 9723 that divides 9708 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9708 and 9723. The biggest common factor number is the GCF number.
So the greatest common factor 9708 and 9723 is 3.

Also check out the Least Common Multiple of 9708 and 9723