What are the divisors of 9155?

1, 5, 1831, 9155

There is a total of 4 positive divisors.
The sum of these divisors is 10992.
The arithmetic mean is 2748.

4 odd divisors

1, 5, 1831, 9155

How to compute the divisors of 9155?

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 9155 by each of the numbers from 1 to 9155 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)

9155 / 1 = 9155 (the remainder is 0, so 1 is a divisor of 9155)
9155 / 2 = 4577.5 (the remainder is 1, so 2 is not a divisor of 9155)
9155 / 3 = 3051.6666666667 (the remainder is 2, so 3 is not a divisor of 9155)
...
9155 / 9154 = 1.0001092418615 (the remainder is 1, so 9154 is not a divisor of 9155)
9155 / 9155 = 1 (the remainder is 0, so 9155 is a divisor of 9155)

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 9155 (i.e. 95.681764197782). 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 $\frac{N}{d} = D$ )

9155 / 1 = 9155 (the remainder is 0, so 1 and 9155 are divisors of 9155)
9155 / 2 = 4577.5 (the remainder is 1, so 2 is not a divisor of 9155)
9155 / 3 = 3051.6666666667 (the remainder is 2, so 3 is not a divisor of 9155)
...
9155 / 94 = 97.393617021277 (the remainder is 37, so 94 is not a divisor of 9155)
9155 / 95 = 96.368421052632 (the remainder is 35, so 95 is not a divisor of 9155)