What are the divisors of 1092?

1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546, 1092

There is a total of 24 positive divisors.
The sum of these divisors is 3136.
The arithmetic mean is 130.66666666667.

16 even divisors

2, 4, 6, 12, 14, 26, 28, 42, 52, 78, 84, 156, 182, 364, 546, 1092

8 odd divisors

1, 3, 7, 13, 21, 39, 91, 273

How to compute the divisors of 1092?

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 1092 by each of the numbers from 1 to 1092 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)

1092 / 1 = 1092 (the remainder is 0, so 1 is a divisor of 1092)
1092 / 2 = 546 (the remainder is 0, so 2 is a divisor of 1092)
1092 / 3 = 364 (the remainder is 0, so 3 is a divisor of 1092)
...
1092 / 1091 = 1.0009165902841 (the remainder is 1, so 1091 is not a divisor of 1092)
1092 / 1092 = 1 (the remainder is 0, so 1092 is a divisor of 1092)

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 1092 (i.e. 33.045423283717). 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 $\frac{N}{d} = D$ )

1092 / 1 = 1092 (the remainder is 0, so 1 and 1092 are divisors of 1092)
1092 / 2 = 546 (the remainder is 0, so 2 and 546 are divisors of 1092)
1092 / 3 = 364 (the remainder is 0, so 3 and 364 are divisors of 1092)
...
1092 / 32 = 34.125 (the remainder is 4, so 32 is not a divisor of 1092)
1092 / 33 = 33.090909090909 (the remainder is 3, so 33 is not a divisor of 1092)