What are the divisors of 8087?

1, 8087

There is a total of 2 positive divisors.
The sum of these divisors is 8088.
The arithmetic mean is 4044.

2 odd divisors

1, 8087

How to compute the divisors of 8087?

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 8087 by each of the numbers from 1 to 8087 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)

8087 / 1 = 8087 (the remainder is 0, so 1 is a divisor of 8087)
8087 / 2 = 4043.5 (the remainder is 1, so 2 is not a divisor of 8087)
8087 / 3 = 2695.6666666667 (the remainder is 2, so 3 is not a divisor of 8087)
...
8087 / 8086 = 1.0001236705417 (the remainder is 1, so 8086 is not a divisor of 8087)
8087 / 8087 = 1 (the remainder is 0, so 8087 is a divisor of 8087)

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 8087 (i.e. 89.927748776448). 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 $\frac{N}{d} = D$ )

8087 / 1 = 8087 (the remainder is 0, so 1 and 8087 are divisors of 8087)
8087 / 2 = 4043.5 (the remainder is 1, so 2 is not a divisor of 8087)
8087 / 3 = 2695.6666666667 (the remainder is 2, so 3 is not a divisor of 8087)
...
8087 / 88 = 91.897727272727 (the remainder is 79, so 88 is not a divisor of 8087)
8087 / 89 = 90.865168539326 (the remainder is 77, so 89 is not a divisor of 8087)