What are the divisors of 5581?

1, 5581

There is a total of 2 positive divisors.
The sum of these divisors is 5582.
The arithmetic mean is 2791.

2 odd divisors

1, 5581

How to compute the divisors of 5581?

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 5581 by each of the numbers from 1 to 5581 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)

5581 / 1 = 5581 (the remainder is 0, so 1 is a divisor of 5581)
5581 / 2 = 2790.5 (the remainder is 1, so 2 is not a divisor of 5581)
5581 / 3 = 1860.3333333333 (the remainder is 1, so 3 is not a divisor of 5581)
...
5581 / 5580 = 1.0001792114695 (the remainder is 1, so 5580 is not a divisor of 5581)
5581 / 5581 = 1 (the remainder is 0, so 5581 is a divisor of 5581)

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 5581 (i.e. 74.706090782479). 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 $\frac{N}{d} = D$ )

5581 / 1 = 5581 (the remainder is 0, so 1 and 5581 are divisors of 5581)
5581 / 2 = 2790.5 (the remainder is 1, so 2 is not a divisor of 5581)
5581 / 3 = 1860.3333333333 (the remainder is 1, so 3 is not a divisor of 5581)
...
5581 / 73 = 76.452054794521 (the remainder is 33, so 73 is not a divisor of 5581)
5581 / 74 = 75.418918918919 (the remainder is 31, so 74 is not a divisor of 5581)