What are the divisors of 8187?

1, 3, 2729, 8187

There is a total of 4 positive divisors.
The sum of these divisors is 10920.
The arithmetic mean is 2730.

4 odd divisors

1, 3, 2729, 8187

How to compute the divisors of 8187?

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 8187 by each of the numbers from 1 to 8187 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)

8187 / 1 = 8187 (the remainder is 0, so 1 is a divisor of 8187)
8187 / 2 = 4093.5 (the remainder is 1, so 2 is not a divisor of 8187)
8187 / 3 = 2729 (the remainder is 0, so 3 is a divisor of 8187)
...
8187 / 8186 = 1.000122159785 (the remainder is 1, so 8186 is not a divisor of 8187)
8187 / 8187 = 1 (the remainder is 0, so 8187 is a divisor of 8187)

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 8187 (i.e. 90.482042417266). 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 $\frac{N}{d} = D$ )

8187 / 1 = 8187 (the remainder is 0, so 1 and 8187 are divisors of 8187)
8187 / 2 = 4093.5 (the remainder is 1, so 2 is not a divisor of 8187)
8187 / 3 = 2729 (the remainder is 0, so 3 and 2729 are divisors of 8187)
...
8187 / 89 = 91.988764044944 (the remainder is 88, so 89 is not a divisor of 8187)
8187 / 90 = 90.966666666667 (the remainder is 87, so 90 is not a divisor of 8187)