What are the divisors of 9015?

1, 3, 5, 15, 601, 1803, 3005, 9015

There is a total of 8 positive divisors.
The sum of these divisors is 14448.
The arithmetic mean is 1806.

8 odd divisors

1, 3, 5, 15, 601, 1803, 3005, 9015

How to compute the divisors of 9015?

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 9015 by each of the numbers from 1 to 9015 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)

9015 / 1 = 9015 (the remainder is 0, so 1 is a divisor of 9015)
9015 / 2 = 4507.5 (the remainder is 1, so 2 is not a divisor of 9015)
9015 / 3 = 3005 (the remainder is 0, so 3 is a divisor of 9015)
...
9015 / 9014 = 1.00011093854 (the remainder is 1, so 9014 is not a divisor of 9015)
9015 / 9015 = 1 (the remainder is 0, so 9015 is a divisor of 9015)

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 9015 (i.e. 94.947353833585). 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 $\frac{N}{d} = D$ )

9015 / 1 = 9015 (the remainder is 0, so 1 and 9015 are divisors of 9015)
9015 / 2 = 4507.5 (the remainder is 1, so 2 is not a divisor of 9015)
9015 / 3 = 3005 (the remainder is 0, so 3 and 3005 are divisors of 9015)
...
9015 / 93 = 96.935483870968 (the remainder is 87, so 93 is not a divisor of 9015)
9015 / 94 = 95.904255319149 (the remainder is 85, so 94 is not a divisor of 9015)