What are the divisors of 8287?

1, 8287

There is a total of 2 positive divisors.
The sum of these divisors is 8288.
The arithmetic mean is 4144.

2 odd divisors

1, 8287

How to compute the divisors of 8287?

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 8287 by each of the numbers from 1 to 8287 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)

8287 / 1 = 8287 (the remainder is 0, so 1 is a divisor of 8287)
8287 / 2 = 4143.5 (the remainder is 1, so 2 is not a divisor of 8287)
8287 / 3 = 2762.3333333333 (the remainder is 1, so 3 is not a divisor of 8287)
...
8287 / 8286 = 1.0001206854936 (the remainder is 1, so 8286 is not a divisor of 8287)
8287 / 8287 = 1 (the remainder is 0, so 8287 is a divisor of 8287)

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 8287 (i.e. 91.032961063562). 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 $\frac{N}{d} = D$ )

8287 / 1 = 8287 (the remainder is 0, so 1 and 8287 are divisors of 8287)
8287 / 2 = 4143.5 (the remainder is 1, so 2 is not a divisor of 8287)
8287 / 3 = 2762.3333333333 (the remainder is 1, so 3 is not a divisor of 8287)
...
8287 / 90 = 92.077777777778 (the remainder is 7, so 90 is not a divisor of 8287)
8287 / 91 = 91.065934065934 (the remainder is 6, so 91 is not a divisor of 8287)