What are the divisors of 5543?

1, 23, 241, 5543

There is a total of 4 positive divisors.
The sum of these divisors is 5808.
The arithmetic mean is 1452.

4 odd divisors

1, 23, 241, 5543

How to compute the divisors of 5543?

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 5543 by each of the numbers from 1 to 5543 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)

5543 / 1 = 5543 (the remainder is 0, so 1 is a divisor of 5543)
5543 / 2 = 2771.5 (the remainder is 1, so 2 is not a divisor of 5543)
5543 / 3 = 1847.6666666667 (the remainder is 2, so 3 is not a divisor of 5543)
...
5543 / 5542 = 1.0001804402743 (the remainder is 1, so 5542 is not a divisor of 5543)
5543 / 5543 = 1 (the remainder is 0, so 5543 is a divisor of 5543)

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 5543 (i.e. 74.451326381737). 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 $\frac{N}{d} = D$ )

5543 / 1 = 5543 (the remainder is 0, so 1 and 5543 are divisors of 5543)
5543 / 2 = 2771.5 (the remainder is 1, so 2 is not a divisor of 5543)
5543 / 3 = 1847.6666666667 (the remainder is 2, so 3 is not a divisor of 5543)
...
5543 / 73 = 75.931506849315 (the remainder is 68, so 73 is not a divisor of 5543)
5543 / 74 = 74.905405405405 (the remainder is 67, so 74 is not a divisor of 5543)