What are the divisors of 9162?

1, 2, 3, 6, 9, 18, 509, 1018, 1527, 3054, 4581, 9162

There is a total of 12 positive divisors.
The sum of these divisors is 19890.
The arithmetic mean is 1657.5.

6 even divisors

2, 6, 18, 1018, 3054, 9162

6 odd divisors

1, 3, 9, 509, 1527, 4581

How to compute the divisors of 9162?

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 9162 by each of the numbers from 1 to 9162 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)

9162 / 1 = 9162 (the remainder is 0, so 1 is a divisor of 9162)
9162 / 2 = 4581 (the remainder is 0, so 2 is a divisor of 9162)
9162 / 3 = 3054 (the remainder is 0, so 3 is a divisor of 9162)
...
9162 / 9161 = 1.0001091583888 (the remainder is 1, so 9161 is not a divisor of 9162)
9162 / 9162 = 1 (the remainder is 0, so 9162 is a divisor of 9162)

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 9162 (i.e. 95.718336801263). 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 $\frac{N}{d} = D$ )

9162 / 1 = 9162 (the remainder is 0, so 1 and 9162 are divisors of 9162)
9162 / 2 = 4581 (the remainder is 0, so 2 and 4581 are divisors of 9162)
9162 / 3 = 3054 (the remainder is 0, so 3 and 3054 are divisors of 9162)
...
9162 / 94 = 97.468085106383 (the remainder is 44, so 94 is not a divisor of 9162)
9162 / 95 = 96.442105263158 (the remainder is 42, so 95 is not a divisor of 9162)