What are the divisors of 5735?

1, 5, 31, 37, 155, 185, 1147, 5735

There is a total of 8 positive divisors.
The sum of these divisors is 7296.
The arithmetic mean is 912.

8 odd divisors

1, 5, 31, 37, 155, 185, 1147, 5735

How to compute the divisors of 5735?

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 5735 by each of the numbers from 1 to 5735 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)

5735 / 1 = 5735 (the remainder is 0, so 1 is a divisor of 5735)
5735 / 2 = 2867.5 (the remainder is 1, so 2 is not a divisor of 5735)
5735 / 3 = 1911.6666666667 (the remainder is 2, so 3 is not a divisor of 5735)
...
5735 / 5734 = 1.0001743983258 (the remainder is 1, so 5734 is not a divisor of 5735)
5735 / 5735 = 1 (the remainder is 0, so 5735 is a divisor of 5735)

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 5735 (i.e. 75.729782780621). 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 $\frac{N}{d} = D$ )

5735 / 1 = 5735 (the remainder is 0, so 1 and 5735 are divisors of 5735)
5735 / 2 = 2867.5 (the remainder is 1, so 2 is not a divisor of 5735)
5735 / 3 = 1911.6666666667 (the remainder is 2, so 3 is not a divisor of 5735)
...
5735 / 74 = 77.5 (the remainder is 37, so 74 is not a divisor of 5735)
5735 / 75 = 76.466666666667 (the remainder is 35, so 75 is not a divisor of 5735)