What is the Greatest Common Factor of 9729 and 9744?

Greatest common factor (GCF) of 9729 and 9744 is 3.

GCF(9729,9744) = 3

We will now calculate the prime factors of 9729 and 9744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9729 and 9744.

How to find the GCF of 9729 and 9744?

We will first find the prime factorization of 9729 and 9744. After we will calculate the factors of 9729 and 9744 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 9744

Prime factors of 9744 are 2, 3, 7, 29. Prime factorization of 9744 in exponential form is:

9744 = 2⁴ × 3¹ × 7¹ × 29¹

Step-3: Factors of 9729

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

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

Step-4: Factors of 9744

List of positive integer factors of 9744 that divides 9729 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 42, 48, 56, 58, 84, 87, 112, 116, 168, 174, 203, 232, 336, 348, 406, 464, 609, 696, 812, 1218, 1392, 1624, 2436, 3248, 4872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9729 and 9744. The biggest common factor number is the GCF number.
So the greatest common factor 9729 and 9744 is 3.

Also check out the Least Common Multiple of 9729 and 9744