What are the divisors of 8188?

1, 2, 4, 23, 46, 89, 92, 178, 356, 2047, 4094, 8188

There is a total of 12 positive divisors.
The sum of these divisors is 15120.
The arithmetic mean is 1260.

8 even divisors

2, 4, 46, 92, 178, 356, 4094, 8188

4 odd divisors

1, 23, 89, 2047

How to compute the divisors of 8188?

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 8188 by each of the numbers from 1 to 8188 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)

8188 / 1 = 8188 (the remainder is 0, so 1 is a divisor of 8188)
8188 / 2 = 4094 (the remainder is 0, so 2 is a divisor of 8188)
8188 / 3 = 2729.3333333333 (the remainder is 1, so 3 is not a divisor of 8188)
...
8188 / 8187 = 1.0001221448638 (the remainder is 1, so 8187 is not a divisor of 8188)
8188 / 8188 = 1 (the remainder is 0, so 8188 is a divisor of 8188)

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 8188 (i.e. 90.487568206909). 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 $\frac{N}{d} = D$ )

8188 / 1 = 8188 (the remainder is 0, so 1 and 8188 are divisors of 8188)
8188 / 2 = 4094 (the remainder is 0, so 2 and 4094 are divisors of 8188)
8188 / 3 = 2729.3333333333 (the remainder is 1, so 3 is not a divisor of 8188)
...
8188 / 89 = 92 (the remainder is 0, so 89 and 92 are divisors of 8188)
8188 / 90 = 90.977777777778 (the remainder is 88, so 90 is not a divisor of 8188)