What are the divisors of 9060?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 151, 302, 453, 604, 755, 906, 1510, 1812, 2265, 3020, 4530, 9060

There is a total of 24 positive divisors.
The sum of these divisors is 25536.
The arithmetic mean is 1064.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 302, 604, 906, 1510, 1812, 3020, 4530, 9060

8 odd divisors

1, 3, 5, 15, 151, 453, 755, 2265

How to compute the divisors of 9060?

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 9060 by each of the numbers from 1 to 9060 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)

9060 / 1 = 9060 (the remainder is 0, so 1 is a divisor of 9060)
9060 / 2 = 4530 (the remainder is 0, so 2 is a divisor of 9060)
9060 / 3 = 3020 (the remainder is 0, so 3 is a divisor of 9060)
...
9060 / 9059 = 1.00011038746 (the remainder is 1, so 9059 is not a divisor of 9060)
9060 / 9060 = 1 (the remainder is 0, so 9060 is a divisor of 9060)

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 9060 (i.e. 95.184032274326). 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 $\frac{N}{d} = D$ )

9060 / 1 = 9060 (the remainder is 0, so 1 and 9060 are divisors of 9060)
9060 / 2 = 4530 (the remainder is 0, so 2 and 4530 are divisors of 9060)
9060 / 3 = 3020 (the remainder is 0, so 3 and 3020 are divisors of 9060)
...
9060 / 94 = 96.382978723404 (the remainder is 36, so 94 is not a divisor of 9060)
9060 / 95 = 95.368421052632 (the remainder is 35, so 95 is not a divisor of 9060)