What are the divisors of 1083?

1, 3, 19, 57, 361, 1083

There is a total of 6 positive divisors.
The sum of these divisors is 1524.
The arithmetic mean is 254.

6 odd divisors

1, 3, 19, 57, 361, 1083

How to compute the divisors of 1083?

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 1083 by each of the numbers from 1 to 1083 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)

1083 / 1 = 1083 (the remainder is 0, so 1 is a divisor of 1083)
1083 / 2 = 541.5 (the remainder is 1, so 2 is not a divisor of 1083)
1083 / 3 = 361 (the remainder is 0, so 3 is a divisor of 1083)
...
1083 / 1082 = 1.0009242144177 (the remainder is 1, so 1082 is not a divisor of 1083)
1083 / 1083 = 1 (the remainder is 0, so 1083 is a divisor of 1083)

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 1083 (i.e. 32.908965343809). 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 $\frac{N}{d} = D$ )

1083 / 1 = 1083 (the remainder is 0, so 1 and 1083 are divisors of 1083)
1083 / 2 = 541.5 (the remainder is 1, so 2 is not a divisor of 1083)
1083 / 3 = 361 (the remainder is 0, so 3 and 361 are divisors of 1083)
...
1083 / 31 = 34.935483870968 (the remainder is 29, so 31 is not a divisor of 1083)
1083 / 32 = 33.84375 (the remainder is 27, so 32 is not a divisor of 1083)