What are the divisors of 1165?

1, 5, 233, 1165

There is a total of 4 positive divisors.
The sum of these divisors is 1404.
The arithmetic mean is 351.

4 odd divisors

1, 5, 233, 1165

How to compute the divisors of 1165?

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 1165 by each of the numbers from 1 to 1165 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)

1165 / 1 = 1165 (the remainder is 0, so 1 is a divisor of 1165)
1165 / 2 = 582.5 (the remainder is 1, so 2 is not a divisor of 1165)
1165 / 3 = 388.33333333333 (the remainder is 1, so 3 is not a divisor of 1165)
...
1165 / 1164 = 1.0008591065292 (the remainder is 1, so 1164 is not a divisor of 1165)
1165 / 1165 = 1 (the remainder is 0, so 1165 is a divisor of 1165)

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 1165 (i.e. 34.132096331752). 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 $\frac{N}{d} = D$ )

1165 / 1 = 1165 (the remainder is 0, so 1 and 1165 are divisors of 1165)
1165 / 2 = 582.5 (the remainder is 1, so 2 is not a divisor of 1165)
1165 / 3 = 388.33333333333 (the remainder is 1, so 3 is not a divisor of 1165)
...
1165 / 33 = 35.30303030303 (the remainder is 10, so 33 is not a divisor of 1165)
1165 / 34 = 34.264705882353 (the remainder is 9, so 34 is not a divisor of 1165)