What are the divisors of 9195?

1, 3, 5, 15, 613, 1839, 3065, 9195

There is a total of 8 positive divisors.
The sum of these divisors is 14736.
The arithmetic mean is 1842.

8 odd divisors

1, 3, 5, 15, 613, 1839, 3065, 9195

How to compute the divisors of 9195?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 9195 by each of the numbers from 1 to 9195 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

9195 / 1 = 9195 (the remainder is 0, so 1 is a divisor of 9195)
9195 / 2 = 4597.5 (the remainder is 1, so 2 is not a divisor of 9195)
9195 / 3 = 3065 (the remainder is 0, so 3 is a divisor of 9195)
...
9195 / 9194 = 1.0001087665869 (the remainder is 1, so 9194 is not a divisor of 9195)
9195 / 9195 = 1 (the remainder is 0, so 9195 is a divisor of 9195)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 9195 (i.e. 95.890562622189). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

9195 / 1 = 9195 (the remainder is 0, so 1 and 9195 are divisors of 9195)
9195 / 2 = 4597.5 (the remainder is 1, so 2 is not a divisor of 9195)
9195 / 3 = 3065 (the remainder is 0, so 3 and 3065 are divisors of 9195)
...
9195 / 94 = 97.81914893617 (the remainder is 77, so 94 is not a divisor of 9195)
9195 / 95 = 96.789473684211 (the remainder is 75, so 95 is not a divisor of 9195)