What are the divisors of 9165?

1, 3, 5, 13, 15, 39, 47, 65, 141, 195, 235, 611, 705, 1833, 3055, 9165

There is a total of 16 positive divisors.
The sum of these divisors is 16128.
The arithmetic mean is 1008.

16 odd divisors

1, 3, 5, 13, 15, 39, 47, 65, 141, 195, 235, 611, 705, 1833, 3055, 9165

How to compute the divisors of 9165?

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 9165 by each of the numbers from 1 to 9165 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)

9165 / 1 = 9165 (the remainder is 0, so 1 is a divisor of 9165)
9165 / 2 = 4582.5 (the remainder is 1, so 2 is not a divisor of 9165)
9165 / 3 = 3055 (the remainder is 0, so 3 is a divisor of 9165)
...
9165 / 9164 = 1.0001091226539 (the remainder is 1, so 9164 is not a divisor of 9165)
9165 / 9165 = 1 (the remainder is 0, so 9165 is a divisor of 9165)

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 9165 (i.e. 95.734006497169). 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 $\frac{N}{d} = D$ )

9165 / 1 = 9165 (the remainder is 0, so 1 and 9165 are divisors of 9165)
9165 / 2 = 4582.5 (the remainder is 1, so 2 is not a divisor of 9165)
9165 / 3 = 3055 (the remainder is 0, so 3 and 3055 are divisors of 9165)
...
9165 / 94 = 97.5 (the remainder is 47, so 94 is not a divisor of 9165)
9165 / 95 = 96.473684210526 (the remainder is 45, so 95 is not a divisor of 9165)