What are the divisors of 9030?

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 43, 70, 86, 105, 129, 210, 215, 258, 301, 430, 602, 645, 903, 1290, 1505, 1806, 3010, 4515, 9030

There is a total of 32 positive divisors.
The sum of these divisors is 25344.
The arithmetic mean is 792.

16 even divisors

2, 6, 10, 14, 30, 42, 70, 86, 210, 258, 430, 602, 1290, 1806, 3010, 9030

16 odd divisors

1, 3, 5, 7, 15, 21, 35, 43, 105, 129, 215, 301, 645, 903, 1505, 4515

How to compute the divisors of 9030?

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 9030 by each of the numbers from 1 to 9030 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)

9030 / 1 = 9030 (the remainder is 0, so 1 is a divisor of 9030)
9030 / 2 = 4515 (the remainder is 0, so 2 is a divisor of 9030)
9030 / 3 = 3010 (the remainder is 0, so 3 is a divisor of 9030)
...
9030 / 9029 = 1.0001107542363 (the remainder is 1, so 9029 is not a divisor of 9030)
9030 / 9030 = 1 (the remainder is 0, so 9030 is a divisor of 9030)

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 9030 (i.e. 95.026312145637). 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 $\frac{N}{d} = D$ )

9030 / 1 = 9030 (the remainder is 0, so 1 and 9030 are divisors of 9030)
9030 / 2 = 4515 (the remainder is 0, so 2 and 4515 are divisors of 9030)
9030 / 3 = 3010 (the remainder is 0, so 3 and 3010 are divisors of 9030)
...
9030 / 94 = 96.063829787234 (the remainder is 6, so 94 is not a divisor of 9030)
9030 / 95 = 95.052631578947 (the remainder is 5, so 95 is not a divisor of 9030)