What are the divisors of 9114?

1, 2, 3, 6, 7, 14, 21, 31, 42, 49, 62, 93, 98, 147, 186, 217, 294, 434, 651, 1302, 1519, 3038, 4557, 9114

There is a total of 24 positive divisors.
The sum of these divisors is 21888.
The arithmetic mean is 912.

12 even divisors

2, 6, 14, 42, 62, 98, 186, 294, 434, 1302, 3038, 9114

12 odd divisors

1, 3, 7, 21, 31, 49, 93, 147, 217, 651, 1519, 4557

How to compute the divisors of 9114?

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 9114 by each of the numbers from 1 to 9114 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)

9114 / 1 = 9114 (the remainder is 0, so 1 is a divisor of 9114)
9114 / 2 = 4557 (the remainder is 0, so 2 is a divisor of 9114)
9114 / 3 = 3038 (the remainder is 0, so 3 is a divisor of 9114)
...
9114 / 9113 = 1.000109733348 (the remainder is 1, so 9113 is not a divisor of 9114)
9114 / 9114 = 1 (the remainder is 0, so 9114 is a divisor of 9114)

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 9114 (i.e. 95.467271878901). 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 $\frac{N}{d} = D$ )

9114 / 1 = 9114 (the remainder is 0, so 1 and 9114 are divisors of 9114)
9114 / 2 = 4557 (the remainder is 0, so 2 and 4557 are divisors of 9114)
9114 / 3 = 3038 (the remainder is 0, so 3 and 3038 are divisors of 9114)
...
9114 / 94 = 96.957446808511 (the remainder is 90, so 94 is not a divisor of 9114)
9114 / 95 = 95.936842105263 (the remainder is 89, so 95 is not a divisor of 9114)