What are the divisors of 8086?

1, 2, 13, 26, 311, 622, 4043, 8086

There is a total of 8 positive divisors.
The sum of these divisors is 13104.
The arithmetic mean is 1638.

4 even divisors

2, 26, 622, 8086

4 odd divisors

1, 13, 311, 4043

How to compute the divisors of 8086?

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 8086 by each of the numbers from 1 to 8086 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)

8086 / 1 = 8086 (the remainder is 0, so 1 is a divisor of 8086)
8086 / 2 = 4043 (the remainder is 0, so 2 is a divisor of 8086)
8086 / 3 = 2695.3333333333 (the remainder is 1, so 3 is not a divisor of 8086)
...
8086 / 8085 = 1.000123685838 (the remainder is 1, so 8085 is not a divisor of 8086)
8086 / 8086 = 1 (the remainder is 0, so 8086 is a divisor of 8086)

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 8086 (i.e. 89.922188585465). 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 $\frac{N}{d} = D$ )

8086 / 1 = 8086 (the remainder is 0, so 1 and 8086 are divisors of 8086)
8086 / 2 = 4043 (the remainder is 0, so 2 and 4043 are divisors of 8086)
8086 / 3 = 2695.3333333333 (the remainder is 1, so 3 is not a divisor of 8086)
...
8086 / 88 = 91.886363636364 (the remainder is 78, so 88 is not a divisor of 8086)
8086 / 89 = 90.85393258427 (the remainder is 76, so 89 is not a divisor of 8086)