What are the divisors of 5789?

1, 7, 827, 5789

There is a total of 4 positive divisors.
The sum of these divisors is 6624.
The arithmetic mean is 1656.

4 odd divisors

1, 7, 827, 5789

How to compute the divisors of 5789?

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 5789 by each of the numbers from 1 to 5789 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)

5789 / 1 = 5789 (the remainder is 0, so 1 is a divisor of 5789)
5789 / 2 = 2894.5 (the remainder is 1, so 2 is not a divisor of 5789)
5789 / 3 = 1929.6666666667 (the remainder is 2, so 3 is not a divisor of 5789)
...
5789 / 5788 = 1.0001727712509 (the remainder is 1, so 5788 is not a divisor of 5789)
5789 / 5789 = 1 (the remainder is 0, so 5789 is a divisor of 5789)

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 5789 (i.e. 76.085478246509). 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 $\frac{N}{d} = D$ )

5789 / 1 = 5789 (the remainder is 0, so 1 and 5789 are divisors of 5789)
5789 / 2 = 2894.5 (the remainder is 1, so 2 is not a divisor of 5789)
5789 / 3 = 1929.6666666667 (the remainder is 2, so 3 is not a divisor of 5789)
...
5789 / 75 = 77.186666666667 (the remainder is 14, so 75 is not a divisor of 5789)
5789 / 76 = 76.171052631579 (the remainder is 13, so 76 is not a divisor of 5789)