What are the divisors of 5761?

1, 7, 823, 5761

There is a total of 4 positive divisors.
The sum of these divisors is 6592.
The arithmetic mean is 1648.

4 odd divisors

1, 7, 823, 5761

How to compute the divisors of 5761?

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 5761 by each of the numbers from 1 to 5761 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)

5761 / 1 = 5761 (the remainder is 0, so 1 is a divisor of 5761)
5761 / 2 = 2880.5 (the remainder is 1, so 2 is not a divisor of 5761)
5761 / 3 = 1920.3333333333 (the remainder is 1, so 3 is not a divisor of 5761)
...
5761 / 5760 = 1.0001736111111 (the remainder is 1, so 5760 is not a divisor of 5761)
5761 / 5761 = 1 (the remainder is 0, so 5761 is a divisor of 5761)

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 5761 (i.e. 75.901251636584). 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 $\frac{N}{d} = D$ )

5761 / 1 = 5761 (the remainder is 0, so 1 and 5761 are divisors of 5761)
5761 / 2 = 2880.5 (the remainder is 1, so 2 is not a divisor of 5761)
5761 / 3 = 1920.3333333333 (the remainder is 1, so 3 is not a divisor of 5761)
...
5761 / 74 = 77.851351351351 (the remainder is 63, so 74 is not a divisor of 5761)
5761 / 75 = 76.813333333333 (the remainder is 61, so 75 is not a divisor of 5761)