What is the Greatest Common Factor of 9735 and 9750?

Greatest common factor (GCF) of 9735 and 9750 is 15.

GCF(9735,9750) = 15

We will now calculate the prime factors of 9735 and 9750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9735 and 9750.

How to find the GCF of 9735 and 9750?

We will first find the prime factorization of 9735 and 9750. After we will calculate the factors of 9735 and 9750 and find the biggest common factor number .

Step-1: Prime Factorization of 9735

Prime factors of 9735 are 3, 5, 11, 59. Prime factorization of 9735 in exponential form is:

9735 = 3¹ × 5¹ × 11¹ × 59¹

Step-2: Prime Factorization of 9750

Prime factors of 9750 are 2, 3, 5, 13. Prime factorization of 9750 in exponential form is:

9750 = 2¹ × 3¹ × 5³ × 13¹

Step-3: Factors of 9735

List of positive integer factors of 9735 that divides 9735 without a remainder.

1, 3, 5, 11, 15, 33, 55, 59, 165, 177, 295, 649, 885, 1947, 3245

Step-4: Factors of 9750

List of positive integer factors of 9750 that divides 9735 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9735 and 9750. The biggest common factor number is the GCF number.
So the greatest common factor 9735 and 9750 is 15.

Also check out the Least Common Multiple of 9735 and 9750