What are the divisors of 5759?

1, 13, 443, 5759

There is a total of 4 positive divisors.
The sum of these divisors is 6216.
The arithmetic mean is 1554.

4 odd divisors

1, 13, 443, 5759

How to compute the divisors of 5759?

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 5759 by each of the numbers from 1 to 5759 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)

5759 / 1 = 5759 (the remainder is 0, so 1 is a divisor of 5759)
5759 / 2 = 2879.5 (the remainder is 1, so 2 is not a divisor of 5759)
5759 / 3 = 1919.6666666667 (the remainder is 2, so 3 is not a divisor of 5759)
...
5759 / 5758 = 1.0001736714137 (the remainder is 1, so 5758 is not a divisor of 5759)
5759 / 5759 = 1 (the remainder is 0, so 5759 is a divisor of 5759)

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 5759 (i.e. 75.888075479617). 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 $\frac{N}{d} = D$ )

5759 / 1 = 5759 (the remainder is 0, so 1 and 5759 are divisors of 5759)
5759 / 2 = 2879.5 (the remainder is 1, so 2 is not a divisor of 5759)
5759 / 3 = 1919.6666666667 (the remainder is 2, so 3 is not a divisor of 5759)
...
5759 / 74 = 77.824324324324 (the remainder is 61, so 74 is not a divisor of 5759)
5759 / 75 = 76.786666666667 (the remainder is 59, so 75 is not a divisor of 5759)