What are the divisors of 5795?

1, 5, 19, 61, 95, 305, 1159, 5795

There is a total of 8 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 930.

8 odd divisors

1, 5, 19, 61, 95, 305, 1159, 5795

How to compute the divisors of 5795?

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 5795 by each of the numbers from 1 to 5795 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)

5795 / 1 = 5795 (the remainder is 0, so 1 is a divisor of 5795)
5795 / 2 = 2897.5 (the remainder is 1, so 2 is not a divisor of 5795)
5795 / 3 = 1931.6666666667 (the remainder is 2, so 3 is not a divisor of 5795)
...
5795 / 5794 = 1.0001725923369 (the remainder is 1, so 5794 is not a divisor of 5795)
5795 / 5795 = 1 (the remainder is 0, so 5795 is a divisor of 5795)

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 5795 (i.e. 76.124897372673). 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 $\frac{N}{d} = D$ )

5795 / 1 = 5795 (the remainder is 0, so 1 and 5795 are divisors of 5795)
5795 / 2 = 2897.5 (the remainder is 1, so 2 is not a divisor of 5795)
5795 / 3 = 1931.6666666667 (the remainder is 2, so 3 is not a divisor of 5795)
...
5795 / 75 = 77.266666666667 (the remainder is 20, so 75 is not a divisor of 5795)
5795 / 76 = 76.25 (the remainder is 19, so 76 is not a divisor of 5795)