What are the divisors of 1611?

1, 3, 9, 179, 537, 1611

There is a total of 6 positive divisors.
The sum of these divisors is 2340.
The arithmetic mean is 390.

6 odd divisors

1, 3, 9, 179, 537, 1611

How to compute the divisors of 1611?

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 1611 by each of the numbers from 1 to 1611 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)

1611 / 1 = 1611 (the remainder is 0, so 1 is a divisor of 1611)
1611 / 2 = 805.5 (the remainder is 1, so 2 is not a divisor of 1611)
1611 / 3 = 537 (the remainder is 0, so 3 is a divisor of 1611)
...
1611 / 1610 = 1.0006211180124 (the remainder is 1, so 1610 is not a divisor of 1611)
1611 / 1611 = 1 (the remainder is 0, so 1611 is a divisor of 1611)

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 1611 (i.e. 40.137264480779). 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 $\frac{N}{d} = D$ )

1611 / 1 = 1611 (the remainder is 0, so 1 and 1611 are divisors of 1611)
1611 / 2 = 805.5 (the remainder is 1, so 2 is not a divisor of 1611)
1611 / 3 = 537 (the remainder is 0, so 3 and 537 are divisors of 1611)
...
1611 / 39 = 41.307692307692 (the remainder is 12, so 39 is not a divisor of 1611)
1611 / 40 = 40.275 (the remainder is 11, so 40 is not a divisor of 1611)