What are the divisors of 1159?

1, 19, 61, 1159

There is a total of 4 positive divisors.
The sum of these divisors is 1240.
The arithmetic mean is 310.

4 odd divisors

1, 19, 61, 1159

How to compute the divisors of 1159?

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 1159 by each of the numbers from 1 to 1159 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)

1159 / 1 = 1159 (the remainder is 0, so 1 is a divisor of 1159)
1159 / 2 = 579.5 (the remainder is 1, so 2 is not a divisor of 1159)
1159 / 3 = 386.33333333333 (the remainder is 1, so 3 is not a divisor of 1159)
...
1159 / 1158 = 1.0008635578584 (the remainder is 1, so 1158 is not a divisor of 1159)
1159 / 1159 = 1 (the remainder is 0, so 1159 is a divisor of 1159)

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 1159 (i.e. 34.044089061098). 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 $\frac{N}{d} = D$ )

1159 / 1 = 1159 (the remainder is 0, so 1 and 1159 are divisors of 1159)
1159 / 2 = 579.5 (the remainder is 1, so 2 is not a divisor of 1159)
1159 / 3 = 386.33333333333 (the remainder is 1, so 3 is not a divisor of 1159)
...
1159 / 33 = 35.121212121212 (the remainder is 4, so 33 is not a divisor of 1159)
1159 / 34 = 34.088235294118 (the remainder is 3, so 34 is not a divisor of 1159)