What are the divisors of 1158?

1, 2, 3, 6, 193, 386, 579, 1158

There is a total of 8 positive divisors.
The sum of these divisors is 2328.
The arithmetic mean is 291.

4 even divisors

2, 6, 386, 1158

4 odd divisors

1, 3, 193, 579

How to compute the divisors of 1158?

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 1158 by each of the numbers from 1 to 1158 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)

1158 / 1 = 1158 (the remainder is 0, so 1 is a divisor of 1158)
1158 / 2 = 579 (the remainder is 0, so 2 is a divisor of 1158)
1158 / 3 = 386 (the remainder is 0, so 3 is a divisor of 1158)
...
1158 / 1157 = 1.0008643042351 (the remainder is 1, so 1157 is not a divisor of 1158)
1158 / 1158 = 1 (the remainder is 0, so 1158 is a divisor of 1158)

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 1158 (i.e. 34.029399054347). 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 $\frac{N}{d} = D$ )

1158 / 1 = 1158 (the remainder is 0, so 1 and 1158 are divisors of 1158)
1158 / 2 = 579 (the remainder is 0, so 2 and 579 are divisors of 1158)
1158 / 3 = 386 (the remainder is 0, so 3 and 386 are divisors of 1158)
...
1158 / 33 = 35.090909090909 (the remainder is 3, so 33 is not a divisor of 1158)
1158 / 34 = 34.058823529412 (the remainder is 2, so 34 is not a divisor of 1158)