What is the Greatest Common Factor of 9744 and 9758?

Greatest common factor (GCF) of 9744 and 9758 is 14.

GCF(9744,9758) = 14

We will now calculate the prime factors of 9744 and 9758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9744 and 9758.

How to find the GCF of 9744 and 9758?

We will first find the prime factorization of 9744 and 9758. After we will calculate the factors of 9744 and 9758 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 9758

Prime factors of 9758 are 2, 7, 17, 41. Prime factorization of 9758 in exponential form is:

9758 = 2¹ × 7¹ × 17¹ × 41¹

Step-3: Factors of 9744

List of positive integer factors of 9744 that divides 9744 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

Step-4: Factors of 9758

List of positive integer factors of 9758 that divides 9744 without a remainder.

1, 2, 7, 14, 17, 34, 41, 82, 119, 238, 287, 574, 697, 1394, 4879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9744 and 9758. The biggest common factor number is the GCF number.
So the greatest common factor 9744 and 9758 is 14.

Also check out the Least Common Multiple of 9744 and 9758