What are the divisors of 5741?

1, 5741

There is a total of 2 positive divisors.
The sum of these divisors is 5742.
The arithmetic mean is 2871.

2 odd divisors

1, 5741

How to compute the divisors of 5741?

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 5741 by each of the numbers from 1 to 5741 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)

5741 / 1 = 5741 (the remainder is 0, so 1 is a divisor of 5741)
5741 / 2 = 2870.5 (the remainder is 1, so 2 is not a divisor of 5741)
5741 / 3 = 1913.6666666667 (the remainder is 2, so 3 is not a divisor of 5741)
...
5741 / 5740 = 1.0001742160279 (the remainder is 1, so 5740 is not a divisor of 5741)
5741 / 5741 = 1 (the remainder is 0, so 5741 is a divisor of 5741)

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 5741 (i.e. 75.769386958058). 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 $\frac{N}{d} = D$ )

5741 / 1 = 5741 (the remainder is 0, so 1 and 5741 are divisors of 5741)
5741 / 2 = 2870.5 (the remainder is 1, so 2 is not a divisor of 5741)
5741 / 3 = 1913.6666666667 (the remainder is 2, so 3 is not a divisor of 5741)
...
5741 / 74 = 77.581081081081 (the remainder is 43, so 74 is not a divisor of 5741)
5741 / 75 = 76.546666666667 (the remainder is 41, so 75 is not a divisor of 5741)