What is the Greatest Common Factor of 9765 and 9771?

Greatest common factor (GCF) of 9765 and 9771 is 3.

GCF(9765,9771) = 3

We will now calculate the prime factors of 9765 and 9771, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9765 and 9771.

How to find the GCF of 9765 and 9771?

We will first find the prime factorization of 9765 and 9771. After we will calculate the factors of 9765 and 9771 and find the biggest common factor number .

Step-1: Prime Factorization of 9765

Prime factors of 9765 are 3, 5, 7, 31. Prime factorization of 9765 in exponential form is:

9765 = 3² × 5¹ × 7¹ × 31¹

Step-2: Prime Factorization of 9771

Prime factors of 9771 are 3, 3257. Prime factorization of 9771 in exponential form is:

9771 = 3¹ × 3257¹

Step-3: Factors of 9765

List of positive integer factors of 9765 that divides 9765 without a remainder.

1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279, 315, 465, 651, 1085, 1395, 1953, 3255

Step-4: Factors of 9771

List of positive integer factors of 9771 that divides 9765 without a remainder.

1, 3, 3257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9765 and 9771. The biggest common factor number is the GCF number.
So the greatest common factor 9765 and 9771 is 3.

Also check out the Least Common Multiple of 9765 and 9771