What are the divisors of 1134?

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 378, 567, 1134

There is a total of 20 positive divisors.
The sum of these divisors is 2904.
The arithmetic mean is 145.2.

10 even divisors

2, 6, 14, 18, 42, 54, 126, 162, 378, 1134

10 odd divisors

1, 3, 7, 9, 21, 27, 63, 81, 189, 567

How to compute the divisors of 1134?

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 1134 by each of the numbers from 1 to 1134 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)

1134 / 1 = 1134 (the remainder is 0, so 1 is a divisor of 1134)
1134 / 2 = 567 (the remainder is 0, so 2 is a divisor of 1134)
1134 / 3 = 378 (the remainder is 0, so 3 is a divisor of 1134)
...
1134 / 1133 = 1.0008826125331 (the remainder is 1, so 1133 is not a divisor of 1134)
1134 / 1134 = 1 (the remainder is 0, so 1134 is a divisor of 1134)

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 1134 (i.e. 33.674916480965). 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 $\frac{N}{d} = D$ )

1134 / 1 = 1134 (the remainder is 0, so 1 and 1134 are divisors of 1134)
1134 / 2 = 567 (the remainder is 0, so 2 and 567 are divisors of 1134)
1134 / 3 = 378 (the remainder is 0, so 3 and 378 are divisors of 1134)
...
1134 / 32 = 35.4375 (the remainder is 14, so 32 is not a divisor of 1134)
1134 / 33 = 34.363636363636 (the remainder is 12, so 33 is not a divisor of 1134)