What are the divisors of 1629?

1, 3, 9, 181, 543, 1629

There is a total of 6 positive divisors.
The sum of these divisors is 2366.
The arithmetic mean is 394.33333333333.

6 odd divisors

1, 3, 9, 181, 543, 1629

How to compute the divisors of 1629?

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 1629 by each of the numbers from 1 to 1629 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)

1629 / 1 = 1629 (the remainder is 0, so 1 is a divisor of 1629)
1629 / 2 = 814.5 (the remainder is 1, so 2 is not a divisor of 1629)
1629 / 3 = 543 (the remainder is 0, so 3 is a divisor of 1629)
...
1629 / 1628 = 1.0006142506143 (the remainder is 1, so 1628 is not a divisor of 1629)
1629 / 1629 = 1 (the remainder is 0, so 1629 is a divisor of 1629)

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 1629 (i.e. 40.360872141221). 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 $\frac{N}{d} = D$ )

1629 / 1 = 1629 (the remainder is 0, so 1 and 1629 are divisors of 1629)
1629 / 2 = 814.5 (the remainder is 1, so 2 is not a divisor of 1629)
1629 / 3 = 543 (the remainder is 0, so 3 and 543 are divisors of 1629)
...
1629 / 39 = 41.769230769231 (the remainder is 30, so 39 is not a divisor of 1629)
1629 / 40 = 40.725 (the remainder is 29, so 40 is not a divisor of 1629)