What are the divisors of 9161?

1, 9161

There is a total of 2 positive divisors.
The sum of these divisors is 9162.
The arithmetic mean is 4581.

2 odd divisors

1, 9161

How to compute the divisors of 9161?

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 9161 by each of the numbers from 1 to 9161 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)

9161 / 1 = 9161 (the remainder is 0, so 1 is a divisor of 9161)
9161 / 2 = 4580.5 (the remainder is 1, so 2 is not a divisor of 9161)
9161 / 3 = 3053.6666666667 (the remainder is 2, so 3 is not a divisor of 9161)
...
9161 / 9160 = 1.0001091703057 (the remainder is 1, so 9160 is not a divisor of 9161)
9161 / 9161 = 1 (the remainder is 0, so 9161 is a divisor of 9161)

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 9161 (i.e. 95.713112999212). 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 $\frac{N}{d} = D$ )

9161 / 1 = 9161 (the remainder is 0, so 1 and 9161 are divisors of 9161)
9161 / 2 = 4580.5 (the remainder is 1, so 2 is not a divisor of 9161)
9161 / 3 = 3053.6666666667 (the remainder is 2, so 3 is not a divisor of 9161)
...
9161 / 94 = 97.457446808511 (the remainder is 43, so 94 is not a divisor of 9161)
9161 / 95 = 96.431578947368 (the remainder is 41, so 95 is not a divisor of 9161)