What are the divisors of 5785?

1, 5, 13, 65, 89, 445, 1157, 5785

There is a total of 8 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 945.

8 odd divisors

1, 5, 13, 65, 89, 445, 1157, 5785

How to compute the divisors of 5785?

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 5785 by each of the numbers from 1 to 5785 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)

5785 / 1 = 5785 (the remainder is 0, so 1 is a divisor of 5785)
5785 / 2 = 2892.5 (the remainder is 1, so 2 is not a divisor of 5785)
5785 / 3 = 1928.3333333333 (the remainder is 1, so 3 is not a divisor of 5785)
...
5785 / 5784 = 1.0001728907331 (the remainder is 1, so 5784 is not a divisor of 5785)
5785 / 5785 = 1 (the remainder is 0, so 5785 is a divisor of 5785)

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 5785 (i.e. 76.059187479226). 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 $\frac{N}{d} = D$ )

5785 / 1 = 5785 (the remainder is 0, so 1 and 5785 are divisors of 5785)
5785 / 2 = 2892.5 (the remainder is 1, so 2 is not a divisor of 5785)
5785 / 3 = 1928.3333333333 (the remainder is 1, so 3 is not a divisor of 5785)
...
5785 / 75 = 77.133333333333 (the remainder is 10, so 75 is not a divisor of 5785)
5785 / 76 = 76.118421052632 (the remainder is 9, so 76 is not a divisor of 5785)