What are the divisors of 9132?

1, 2, 3, 4, 6, 12, 761, 1522, 2283, 3044, 4566, 9132

There is a total of 12 positive divisors.
The sum of these divisors is 21336.
The arithmetic mean is 1778.

8 even divisors

2, 4, 6, 12, 1522, 3044, 4566, 9132

4 odd divisors

1, 3, 761, 2283

How to compute the divisors of 9132?

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 9132 by each of the numbers from 1 to 9132 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)

9132 / 1 = 9132 (the remainder is 0, so 1 is a divisor of 9132)
9132 / 2 = 4566 (the remainder is 0, so 2 is a divisor of 9132)
9132 / 3 = 3044 (the remainder is 0, so 3 is a divisor of 9132)
...
9132 / 9131 = 1.0001095170299 (the remainder is 1, so 9131 is not a divisor of 9132)
9132 / 9132 = 1 (the remainder is 0, so 9132 is a divisor of 9132)

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 9132 (i.e. 95.561498523202). 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 $\frac{N}{d} = D$ )

9132 / 1 = 9132 (the remainder is 0, so 1 and 9132 are divisors of 9132)
9132 / 2 = 4566 (the remainder is 0, so 2 and 4566 are divisors of 9132)
9132 / 3 = 3044 (the remainder is 0, so 3 and 3044 are divisors of 9132)
...
9132 / 94 = 97.148936170213 (the remainder is 14, so 94 is not a divisor of 9132)
9132 / 95 = 96.126315789474 (the remainder is 12, so 95 is not a divisor of 9132)