What are the divisors of 8104?

1, 2, 4, 8, 1013, 2026, 4052, 8104

There is a total of 8 positive divisors.
The sum of these divisors is 15210.
The arithmetic mean is 1901.25.

6 even divisors

2, 4, 8, 2026, 4052, 8104

2 odd divisors

1, 1013

How to compute the divisors of 8104?

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 8104 by each of the numbers from 1 to 8104 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)

8104 / 1 = 8104 (the remainder is 0, so 1 is a divisor of 8104)
8104 / 2 = 4052 (the remainder is 0, so 2 is a divisor of 8104)
8104 / 3 = 2701.3333333333 (the remainder is 1, so 3 is not a divisor of 8104)
...
8104 / 8103 = 1.0001234110823 (the remainder is 1, so 8103 is not a divisor of 8104)
8104 / 8104 = 1 (the remainder is 0, so 8104 is a divisor of 8104)

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 8104 (i.e. 90.022219479415). 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 $\frac{N}{d} = D$ )

8104 / 1 = 8104 (the remainder is 0, so 1 and 8104 are divisors of 8104)
8104 / 2 = 4052 (the remainder is 0, so 2 and 4052 are divisors of 8104)
8104 / 3 = 2701.3333333333 (the remainder is 1, so 3 is not a divisor of 8104)
...
8104 / 89 = 91.056179775281 (the remainder is 5, so 89 is not a divisor of 8104)
8104 / 90 = 90.044444444444 (the remainder is 4, so 90 is not a divisor of 8104)