What are the divisors of 5583?

1, 3, 1861, 5583

There is a total of 4 positive divisors.
The sum of these divisors is 7448.
The arithmetic mean is 1862.

4 odd divisors

1, 3, 1861, 5583

How to compute the divisors of 5583?

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 5583 by each of the numbers from 1 to 5583 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)

5583 / 1 = 5583 (the remainder is 0, so 1 is a divisor of 5583)
5583 / 2 = 2791.5 (the remainder is 1, so 2 is not a divisor of 5583)
5583 / 3 = 1861 (the remainder is 0, so 3 is a divisor of 5583)
...
5583 / 5582 = 1.000179147259 (the remainder is 1, so 5582 is not a divisor of 5583)
5583 / 5583 = 1 (the remainder is 0, so 5583 is a divisor of 5583)

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 5583 (i.e. 74.719475372891). 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 $\frac{N}{d} = D$ )

5583 / 1 = 5583 (the remainder is 0, so 1 and 5583 are divisors of 5583)
5583 / 2 = 2791.5 (the remainder is 1, so 2 is not a divisor of 5583)
5583 / 3 = 1861 (the remainder is 0, so 3 and 1861 are divisors of 5583)
...
5583 / 73 = 76.479452054795 (the remainder is 35, so 73 is not a divisor of 5583)
5583 / 74 = 75.445945945946 (the remainder is 33, so 74 is not a divisor of 5583)