What are the divisors of 9180?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 27, 30, 34, 36, 45, 51, 54, 60, 68, 85, 90, 102, 108, 135, 153, 170, 180, 204, 255, 270, 306, 340, 459, 510, 540, 612, 765, 918, 1020, 1530, 1836, 2295, 3060, 4590, 9180

There is a total of 48 positive divisors.
The sum of these divisors is 30240.
The arithmetic mean is 630.

32 even divisors

2, 4, 6, 10, 12, 18, 20, 30, 34, 36, 54, 60, 68, 90, 102, 108, 170, 180, 204, 270, 306, 340, 510, 540, 612, 918, 1020, 1530, 1836, 3060, 4590, 9180

16 odd divisors

1, 3, 5, 9, 15, 17, 27, 45, 51, 85, 135, 153, 255, 459, 765, 2295

How to compute the divisors of 9180?

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 9180 by each of the numbers from 1 to 9180 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)

9180 / 1 = 9180 (the remainder is 0, so 1 is a divisor of 9180)
9180 / 2 = 4590 (the remainder is 0, so 2 is a divisor of 9180)
9180 / 3 = 3060 (the remainder is 0, so 3 is a divisor of 9180)
...
9180 / 9179 = 1.0001089443294 (the remainder is 1, so 9179 is not a divisor of 9180)
9180 / 9180 = 1 (the remainder is 0, so 9180 is a divisor of 9180)

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 9180 (i.e. 95.812316536028). 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 $\frac{N}{d} = D$ )

9180 / 1 = 9180 (the remainder is 0, so 1 and 9180 are divisors of 9180)
9180 / 2 = 4590 (the remainder is 0, so 2 and 4590 are divisors of 9180)
9180 / 3 = 3060 (the remainder is 0, so 3 and 3060 are divisors of 9180)
...
9180 / 94 = 97.659574468085 (the remainder is 62, so 94 is not a divisor of 9180)
9180 / 95 = 96.631578947368 (the remainder is 60, so 95 is not a divisor of 9180)