What are the divisors of 9115?

1, 5, 1823, 9115

There is a total of 4 positive divisors.
The sum of these divisors is 10944.
The arithmetic mean is 2736.

4 odd divisors

1, 5, 1823, 9115

How to compute the divisors of 9115?

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 9115 by each of the numbers from 1 to 9115 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)

9115 / 1 = 9115 (the remainder is 0, so 1 is a divisor of 9115)
9115 / 2 = 4557.5 (the remainder is 1, so 2 is not a divisor of 9115)
9115 / 3 = 3038.3333333333 (the remainder is 1, so 3 is not a divisor of 9115)
...
9115 / 9114 = 1.0001097213079 (the remainder is 1, so 9114 is not a divisor of 9115)
9115 / 9115 = 1 (the remainder is 0, so 9115 is a divisor of 9115)

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 9115 (i.e. 95.47250913221). 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 $\frac{N}{d} = D$ )

9115 / 1 = 9115 (the remainder is 0, so 1 and 9115 are divisors of 9115)
9115 / 2 = 4557.5 (the remainder is 1, so 2 is not a divisor of 9115)
9115 / 3 = 3038.3333333333 (the remainder is 1, so 3 is not a divisor of 9115)
...
9115 / 94 = 96.968085106383 (the remainder is 91, so 94 is not a divisor of 9115)
9115 / 95 = 95.947368421053 (the remainder is 90, so 95 is not a divisor of 9115)