What are the divisors of 5693?

1, 5693

There is a total of 2 positive divisors.
The sum of these divisors is 5694.
The arithmetic mean is 2847.

2 odd divisors

1, 5693

How to compute the divisors of 5693?

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 5693 by each of the numbers from 1 to 5693 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)

5693 / 1 = 5693 (the remainder is 0, so 1 is a divisor of 5693)
5693 / 2 = 2846.5 (the remainder is 1, so 2 is not a divisor of 5693)
5693 / 3 = 1897.6666666667 (the remainder is 2, so 3 is not a divisor of 5693)
...
5693 / 5692 = 1.0001756851722 (the remainder is 1, so 5692 is not a divisor of 5693)
5693 / 5693 = 1 (the remainder is 0, so 5693 is a divisor of 5693)

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 5693 (i.e. 75.451971478551). 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 $\frac{N}{d} = D$ )

5693 / 1 = 5693 (the remainder is 0, so 1 and 5693 are divisors of 5693)
5693 / 2 = 2846.5 (the remainder is 1, so 2 is not a divisor of 5693)
5693 / 3 = 1897.6666666667 (the remainder is 2, so 3 is not a divisor of 5693)
...
5693 / 74 = 76.932432432432 (the remainder is 69, so 74 is not a divisor of 5693)
5693 / 75 = 75.906666666667 (the remainder is 68, so 75 is not a divisor of 5693)