What are the divisors of 8092?

1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 289, 476, 578, 1156, 2023, 4046, 8092

There is a total of 18 positive divisors.
The sum of these divisors is 17192.
The arithmetic mean is 955.11111111111.

12 even divisors

2, 4, 14, 28, 34, 68, 238, 476, 578, 1156, 4046, 8092

6 odd divisors

1, 7, 17, 119, 289, 2023

How to compute the divisors of 8092?

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 8092 by each of the numbers from 1 to 8092 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)

8092 / 1 = 8092 (the remainder is 0, so 1 is a divisor of 8092)
8092 / 2 = 4046 (the remainder is 0, so 2 is a divisor of 8092)
8092 / 3 = 2697.3333333333 (the remainder is 1, so 3 is not a divisor of 8092)
...
8092 / 8091 = 1.0001235941169 (the remainder is 1, so 8091 is not a divisor of 8092)
8092 / 8092 = 1 (the remainder is 0, so 8092 is a divisor of 8092)

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 8092 (i.e. 89.955544576196). 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 $\frac{N}{d} = D$ )

8092 / 1 = 8092 (the remainder is 0, so 1 and 8092 are divisors of 8092)
8092 / 2 = 4046 (the remainder is 0, so 2 and 4046 are divisors of 8092)
8092 / 3 = 2697.3333333333 (the remainder is 1, so 3 is not a divisor of 8092)
...
8092 / 88 = 91.954545454545 (the remainder is 84, so 88 is not a divisor of 8092)
8092 / 89 = 90.921348314607 (the remainder is 82, so 89 is not a divisor of 8092)