What are the divisors of 9235?

1, 5, 1847, 9235

There is a total of 4 positive divisors.
The sum of these divisors is 11088.
The arithmetic mean is 2772.

4 odd divisors

1, 5, 1847, 9235

How to compute the divisors of 9235?

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 9235 by each of the numbers from 1 to 9235 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)

9235 / 1 = 9235 (the remainder is 0, so 1 is a divisor of 9235)
9235 / 2 = 4617.5 (the remainder is 1, so 2 is not a divisor of 9235)
9235 / 3 = 3078.3333333333 (the remainder is 1, so 3 is not a divisor of 9235)
...
9235 / 9234 = 1.0001082954299 (the remainder is 1, so 9234 is not a divisor of 9235)
9235 / 9235 = 1 (the remainder is 0, so 9235 is a divisor of 9235)

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 9235 (i.e. 96.098907381926). 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 $\frac{N}{d} = D$ )

9235 / 1 = 9235 (the remainder is 0, so 1 and 9235 are divisors of 9235)
9235 / 2 = 4617.5 (the remainder is 1, so 2 is not a divisor of 9235)
9235 / 3 = 3078.3333333333 (the remainder is 1, so 3 is not a divisor of 9235)
...
9235 / 95 = 97.210526315789 (the remainder is 20, so 95 is not a divisor of 9235)
9235 / 96 = 96.197916666667 (the remainder is 19, so 96 is not a divisor of 9235)