What are the divisors of 5582?

1, 2, 2791, 5582

There is a total of 4 positive divisors.
The sum of these divisors is 8376.
The arithmetic mean is 2094.

2 even divisors

2, 5582

2 odd divisors

1, 2791

How to compute the divisors of 5582?

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 5582 by each of the numbers from 1 to 5582 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)

5582 / 1 = 5582 (the remainder is 0, so 1 is a divisor of 5582)
5582 / 2 = 2791 (the remainder is 0, so 2 is a divisor of 5582)
5582 / 3 = 1860.6666666667 (the remainder is 2, so 3 is not a divisor of 5582)
...
5582 / 5581 = 1.0001791793585 (the remainder is 1, so 5581 is not a divisor of 5582)
5582 / 5582 = 1 (the remainder is 0, so 5582 is a divisor of 5582)

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 5582 (i.e. 74.712783377411). 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 $\frac{N}{d} = D$ )

5582 / 1 = 5582 (the remainder is 0, so 1 and 5582 are divisors of 5582)
5582 / 2 = 2791 (the remainder is 0, so 2 and 2791 are divisors of 5582)
5582 / 3 = 1860.6666666667 (the remainder is 2, so 3 is not a divisor of 5582)
...
5582 / 73 = 76.465753424658 (the remainder is 34, so 73 is not a divisor of 5582)
5582 / 74 = 75.432432432432 (the remainder is 32, so 74 is not a divisor of 5582)