What are the divisors of 5758?

1, 2, 2879, 5758

There is a total of 4 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 2160.

2 even divisors

2, 5758

2 odd divisors

1, 2879

How to compute the divisors of 5758?

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 5758 by each of the numbers from 1 to 5758 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)

5758 / 1 = 5758 (the remainder is 0, so 1 is a divisor of 5758)
5758 / 2 = 2879 (the remainder is 0, so 2 is a divisor of 5758)
5758 / 3 = 1919.3333333333 (the remainder is 1, so 3 is not a divisor of 5758)
...
5758 / 5757 = 1.0001737015807 (the remainder is 1, so 5757 is not a divisor of 5758)
5758 / 5758 = 1 (the remainder is 0, so 5758 is a divisor of 5758)

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 5758 (i.e. 75.881486543162). 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 $\frac{N}{d} = D$ )

5758 / 1 = 5758 (the remainder is 0, so 1 and 5758 are divisors of 5758)
5758 / 2 = 2879 (the remainder is 0, so 2 and 2879 are divisors of 5758)
5758 / 3 = 1919.3333333333 (the remainder is 1, so 3 is not a divisor of 5758)
...
5758 / 74 = 77.810810810811 (the remainder is 60, so 74 is not a divisor of 5758)
5758 / 75 = 76.773333333333 (the remainder is 58, so 75 is not a divisor of 5758)