What are the divisors of 1068?

1, 2, 3, 4, 6, 12, 89, 178, 267, 356, 534, 1068

There is a total of 12 positive divisors.
The sum of these divisors is 2520.
The arithmetic mean is 210.

8 even divisors

2, 4, 6, 12, 178, 356, 534, 1068

4 odd divisors

1, 3, 89, 267

How to compute the divisors of 1068?

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 1068 by each of the numbers from 1 to 1068 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)

1068 / 1 = 1068 (the remainder is 0, so 1 is a divisor of 1068)
1068 / 2 = 534 (the remainder is 0, so 2 is a divisor of 1068)
1068 / 3 = 356 (the remainder is 0, so 3 is a divisor of 1068)
...
1068 / 1067 = 1.0009372071228 (the remainder is 1, so 1067 is not a divisor of 1068)
1068 / 1068 = 1 (the remainder is 0, so 1068 is a divisor of 1068)

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 1068 (i.e. 32.680269276736). 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 $\frac{N}{d} = D$ )

1068 / 1 = 1068 (the remainder is 0, so 1 and 1068 are divisors of 1068)
1068 / 2 = 534 (the remainder is 0, so 2 and 534 are divisors of 1068)
1068 / 3 = 356 (the remainder is 0, so 3 and 356 are divisors of 1068)
...
1068 / 31 = 34.451612903226 (the remainder is 14, so 31 is not a divisor of 1068)
1068 / 32 = 33.375 (the remainder is 12, so 32 is not a divisor of 1068)