What are the divisors of 1163?

1, 1163

There is a total of 2 positive divisors.
The sum of these divisors is 1164.
The arithmetic mean is 582.

2 odd divisors

1, 1163

How to compute the divisors of 1163?

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 1163 by each of the numbers from 1 to 1163 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)

1163 / 1 = 1163 (the remainder is 0, so 1 is a divisor of 1163)
1163 / 2 = 581.5 (the remainder is 1, so 2 is not a divisor of 1163)
1163 / 3 = 387.66666666667 (the remainder is 2, so 3 is not a divisor of 1163)
...
1163 / 1162 = 1.0008605851979 (the remainder is 1, so 1162 is not a divisor of 1163)
1163 / 1163 = 1 (the remainder is 0, so 1163 is a divisor of 1163)

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 1163 (i.e. 34.10278580996). 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 $\frac{N}{d} = D$ )

1163 / 1 = 1163 (the remainder is 0, so 1 and 1163 are divisors of 1163)
1163 / 2 = 581.5 (the remainder is 1, so 2 is not a divisor of 1163)
1163 / 3 = 387.66666666667 (the remainder is 2, so 3 is not a divisor of 1163)
...
1163 / 33 = 35.242424242424 (the remainder is 8, so 33 is not a divisor of 1163)
1163 / 34 = 34.205882352941 (the remainder is 7, so 34 is not a divisor of 1163)