What are the divisors of 5638?

1, 2, 2819, 5638

There is a total of 4 positive divisors.
The sum of these divisors is 8460.
The arithmetic mean is 2115.

2 even divisors

2, 5638

2 odd divisors

1, 2819

How to compute the divisors of 5638?

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 5638 by each of the numbers from 1 to 5638 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)

5638 / 1 = 5638 (the remainder is 0, so 1 is a divisor of 5638)
5638 / 2 = 2819 (the remainder is 0, so 2 is a divisor of 5638)
5638 / 3 = 1879.3333333333 (the remainder is 1, so 3 is not a divisor of 5638)
...
5638 / 5637 = 1.0001773993259 (the remainder is 1, so 5637 is not a divisor of 5638)
5638 / 5638 = 1 (the remainder is 0, so 5638 is a divisor of 5638)

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 5638 (i.e. 75.086616650373). 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 $\frac{N}{d} = D$ )

5638 / 1 = 5638 (the remainder is 0, so 1 and 5638 are divisors of 5638)
5638 / 2 = 2819 (the remainder is 0, so 2 and 2819 are divisors of 5638)
5638 / 3 = 1879.3333333333 (the remainder is 1, so 3 is not a divisor of 5638)
...
5638 / 74 = 76.189189189189 (the remainder is 14, so 74 is not a divisor of 5638)
5638 / 75 = 75.173333333333 (the remainder is 13, so 75 is not a divisor of 5638)