What are the divisors of 9185?

1, 5, 11, 55, 167, 835, 1837, 9185

There is a total of 8 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 1512.

8 odd divisors

1, 5, 11, 55, 167, 835, 1837, 9185

How to compute the divisors of 9185?

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 9185 by each of the numbers from 1 to 9185 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)

9185 / 1 = 9185 (the remainder is 0, so 1 is a divisor of 9185)
9185 / 2 = 4592.5 (the remainder is 1, so 2 is not a divisor of 9185)
9185 / 3 = 3061.6666666667 (the remainder is 2, so 3 is not a divisor of 9185)
...
9185 / 9184 = 1.0001088850174 (the remainder is 1, so 9184 is not a divisor of 9185)
9185 / 9185 = 1 (the remainder is 0, so 9185 is a divisor of 9185)

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 9185 (i.e. 95.838405662866). 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 $\frac{N}{d} = D$ )

9185 / 1 = 9185 (the remainder is 0, so 1 and 9185 are divisors of 9185)
9185 / 2 = 4592.5 (the remainder is 1, so 2 is not a divisor of 9185)
9185 / 3 = 3061.6666666667 (the remainder is 2, so 3 is not a divisor of 9185)
...
9185 / 94 = 97.712765957447 (the remainder is 67, so 94 is not a divisor of 9185)
9185 / 95 = 96.684210526316 (the remainder is 65, so 95 is not a divisor of 9185)