What are the divisors of 5739?

1, 3, 1913, 5739

There is a total of 4 positive divisors.
The sum of these divisors is 7656.
The arithmetic mean is 1914.

4 odd divisors

1, 3, 1913, 5739

How to compute the divisors of 5739?

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 5739 by each of the numbers from 1 to 5739 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)

5739 / 1 = 5739 (the remainder is 0, so 1 is a divisor of 5739)
5739 / 2 = 2869.5 (the remainder is 1, so 2 is not a divisor of 5739)
5739 / 3 = 1913 (the remainder is 0, so 3 is a divisor of 5739)
...
5739 / 5738 = 1.0001742767515 (the remainder is 1, so 5738 is not a divisor of 5739)
5739 / 5739 = 1 (the remainder is 0, so 5739 is a divisor of 5739)

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 5739 (i.e. 75.756187866075). 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 $\frac{N}{d} = D$ )

5739 / 1 = 5739 (the remainder is 0, so 1 and 5739 are divisors of 5739)
5739 / 2 = 2869.5 (the remainder is 1, so 2 is not a divisor of 5739)
5739 / 3 = 1913 (the remainder is 0, so 3 and 1913 are divisors of 5739)
...
5739 / 74 = 77.554054054054 (the remainder is 41, so 74 is not a divisor of 5739)
5739 / 75 = 76.52 (the remainder is 39, so 75 is not a divisor of 5739)