What are the divisors of 8044?

1, 2, 4, 2011, 4022, 8044

There is a total of 6 positive divisors.
The sum of these divisors is 14084.
The arithmetic mean is 2347.3333333333.

4 even divisors

2, 4, 4022, 8044

2 odd divisors

1, 2011

How to compute the divisors of 8044?

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 8044 by each of the numbers from 1 to 8044 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)

8044 / 1 = 8044 (the remainder is 0, so 1 is a divisor of 8044)
8044 / 2 = 4022 (the remainder is 0, so 2 is a divisor of 8044)
8044 / 3 = 2681.3333333333 (the remainder is 1, so 3 is not a divisor of 8044)
...
8044 / 8043 = 1.000124331717 (the remainder is 1, so 8043 is not a divisor of 8044)
8044 / 8044 = 1 (the remainder is 0, so 8044 is a divisor of 8044)

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 8044 (i.e. 89.688349299115). 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 $\frac{N}{d} = D$ )

8044 / 1 = 8044 (the remainder is 0, so 1 and 8044 are divisors of 8044)
8044 / 2 = 4022 (the remainder is 0, so 2 and 4022 are divisors of 8044)
8044 / 3 = 2681.3333333333 (the remainder is 1, so 3 is not a divisor of 8044)
...
8044 / 88 = 91.409090909091 (the remainder is 36, so 88 is not a divisor of 8044)
8044 / 89 = 90.38202247191 (the remainder is 34, so 89 is not a divisor of 8044)