What are the divisors of 9087?

1, 3, 13, 39, 233, 699, 3029, 9087

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

8 odd divisors

1, 3, 13, 39, 233, 699, 3029, 9087

How to compute the divisors of 9087?

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 9087 by each of the numbers from 1 to 9087 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)

9087 / 1 = 9087 (the remainder is 0, so 1 is a divisor of 9087)
9087 / 2 = 4543.5 (the remainder is 1, so 2 is not a divisor of 9087)
9087 / 3 = 3029 (the remainder is 0, so 3 is a divisor of 9087)
...
9087 / 9086 = 1.0001100594321 (the remainder is 1, so 9086 is not a divisor of 9087)
9087 / 9087 = 1 (the remainder is 0, so 9087 is a divisor of 9087)

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 9087 (i.e. 95.325757274726). 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 $\frac{N}{d} = D$ )

9087 / 1 = 9087 (the remainder is 0, so 1 and 9087 are divisors of 9087)
9087 / 2 = 4543.5 (the remainder is 1, so 2 is not a divisor of 9087)
9087 / 3 = 3029 (the remainder is 0, so 3 and 3029 are divisors of 9087)
...
9087 / 94 = 96.670212765957 (the remainder is 63, so 94 is not a divisor of 9087)
9087 / 95 = 95.652631578947 (the remainder is 62, so 95 is not a divisor of 9087)