What are the divisors of 2043?

1, 3, 9, 227, 681, 2043

There is a total of 6 positive divisors.
The sum of these divisors is 2964.
The arithmetic mean is 494.

6 odd divisors

1, 3, 9, 227, 681, 2043

How to compute the divisors of 2043?

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 2043 by each of the numbers from 1 to 2043 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)

2043 / 1 = 2043 (the remainder is 0, so 1 is a divisor of 2043)
2043 / 2 = 1021.5 (the remainder is 1, so 2 is not a divisor of 2043)
2043 / 3 = 681 (the remainder is 0, so 3 is a divisor of 2043)
...
2043 / 2042 = 1.0004897159647 (the remainder is 1, so 2042 is not a divisor of 2043)
2043 / 2043 = 1 (the remainder is 0, so 2043 is a divisor of 2043)

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 2043 (i.e. 45.199557519958). 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 $\frac{N}{d} = D$ )

2043 / 1 = 2043 (the remainder is 0, so 1 and 2043 are divisors of 2043)
2043 / 2 = 1021.5 (the remainder is 1, so 2 is not a divisor of 2043)
2043 / 3 = 681 (the remainder is 0, so 3 and 681 are divisors of 2043)
...
2043 / 44 = 46.431818181818 (the remainder is 19, so 44 is not a divisor of 2043)
2043 / 45 = 45.4 (the remainder is 18, so 45 is not a divisor of 2043)