What is the Greatest Common Factor of 9765 and 9780?

Greatest common factor (GCF) of 9765 and 9780 is 15.

GCF(9765,9780) = 15

We will now calculate the prime factors of 9765 and 9780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9765 and 9780.

How to find the GCF of 9765 and 9780?

We will first find the prime factorization of 9765 and 9780. After we will calculate the factors of 9765 and 9780 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 9780

Prime factors of 9780 are 2, 3, 5, 163. Prime factorization of 9780 in exponential form is:

9780 = 2² × 3¹ × 5¹ × 163¹

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 9780

List of positive integer factors of 9780 that divides 9765 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 163, 326, 489, 652, 815, 978, 1630, 1956, 2445, 3260, 4890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9765 and 9780. The biggest common factor number is the GCF number.
So the greatest common factor 9765 and 9780 is 15.

Also check out the Least Common Multiple of 9765 and 9780