What are the divisors of 9618?

1, 2, 3, 6, 7, 14, 21, 42, 229, 458, 687, 1374, 1603, 3206, 4809, 9618

There is a total of 16 positive divisors.
The sum of these divisors is 22080.
The arithmetic mean is 1380.

8 even divisors

2, 6, 14, 42, 458, 1374, 3206, 9618

8 odd divisors

1, 3, 7, 21, 229, 687, 1603, 4809

How to compute the divisors of 9618?

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 9618 by each of the numbers from 1 to 9618 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)

9618 / 1 = 9618 (the remainder is 0, so 1 is a divisor of 9618)
9618 / 2 = 4809 (the remainder is 0, so 2 is a divisor of 9618)
9618 / 3 = 3206 (the remainder is 0, so 3 is a divisor of 9618)
...
9618 / 9617 = 1.0001039825309 (the remainder is 1, so 9617 is not a divisor of 9618)
9618 / 9618 = 1 (the remainder is 0, so 9618 is a divisor of 9618)

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 9618 (i.e. 98.071402559564). 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 $\frac{N}{d} = D$ )

9618 / 1 = 9618 (the remainder is 0, so 1 and 9618 are divisors of 9618)
9618 / 2 = 4809 (the remainder is 0, so 2 and 4809 are divisors of 9618)
9618 / 3 = 3206 (the remainder is 0, so 3 and 3206 are divisors of 9618)
...
9618 / 97 = 99.154639175258 (the remainder is 15, so 97 is not a divisor of 9618)
9618 / 98 = 98.142857142857 (the remainder is 14, so 98 is not a divisor of 9618)