What is the Greatest Common Factor of 9765 and 9785?

Greatest common factor (GCF) of 9765 and 9785 is 5.

GCF(9765,9785) = 5

We will now calculate the prime factors of 9765 and 9785, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9765 and 9785.

How to find the GCF of 9765 and 9785?

We will first find the prime factorization of 9765 and 9785. After we will calculate the factors of 9765 and 9785 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 9785

Prime factors of 9785 are 5, 19, 103. Prime factorization of 9785 in exponential form is:

9785 = 5¹ × 19¹ × 103¹

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 9785

List of positive integer factors of 9785 that divides 9765 without a remainder.

1, 5, 19, 95, 103, 515, 1957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9765 and 9785. The biggest common factor number is the GCF number.
So the greatest common factor 9765 and 9785 is 5.

Also check out the Least Common Multiple of 9765 and 9785