What are the divisors of 9158?

1, 2, 19, 38, 241, 482, 4579, 9158

There is a total of 8 positive divisors.
The sum of these divisors is 14520.
The arithmetic mean is 1815.

4 even divisors

2, 38, 482, 9158

4 odd divisors

1, 19, 241, 4579

How to compute the divisors of 9158?

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 9158 by each of the numbers from 1 to 9158 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)

9158 / 1 = 9158 (the remainder is 0, so 1 is a divisor of 9158)
9158 / 2 = 4579 (the remainder is 0, so 2 is a divisor of 9158)
9158 / 3 = 3052.6666666667 (the remainder is 2, so 3 is not a divisor of 9158)
...
9158 / 9157 = 1.0001092060719 (the remainder is 1, so 9157 is not a divisor of 9158)
9158 / 9158 = 1 (the remainder is 0, so 9158 is a divisor of 9158)

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 9158 (i.e. 95.697439882162). 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 $\frac{N}{d} = D$ )

9158 / 1 = 9158 (the remainder is 0, so 1 and 9158 are divisors of 9158)
9158 / 2 = 4579 (the remainder is 0, so 2 and 4579 are divisors of 9158)
9158 / 3 = 3052.6666666667 (the remainder is 2, so 3 is not a divisor of 9158)
...
9158 / 94 = 97.425531914894 (the remainder is 40, so 94 is not a divisor of 9158)
9158 / 95 = 96.4 (the remainder is 38, so 95 is not a divisor of 9158)