What is the Greatest Common Factor of 9765 and 9772?

Greatest common factor (GCF) of 9765 and 9772 is 7.

GCF(9765,9772) = 7

We will now calculate the prime factors of 9765 and 9772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9765 and 9772.

How to find the GCF of 9765 and 9772?

We will first find the prime factorization of 9765 and 9772. After we will calculate the factors of 9765 and 9772 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 9772

Prime factors of 9772 are 2, 7, 349. Prime factorization of 9772 in exponential form is:

9772 = 2² × 7¹ × 349¹

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 9772

List of positive integer factors of 9772 that divides 9765 without a remainder.

1, 2, 4, 7, 14, 28, 349, 698, 1396, 2443, 4886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9765 and 9772. The biggest common factor number is the GCF number.
So the greatest common factor 9765 and 9772 is 7.

Also check out the Least Common Multiple of 9765 and 9772