What are the divisors of 1636?

1, 2, 4, 409, 818, 1636

There is a total of 6 positive divisors.
The sum of these divisors is 2870.
The arithmetic mean is 478.33333333333.

4 even divisors

2, 4, 818, 1636

2 odd divisors

1, 409

How to compute the divisors of 1636?

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 1636 by each of the numbers from 1 to 1636 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)

1636 / 1 = 1636 (the remainder is 0, so 1 is a divisor of 1636)
1636 / 2 = 818 (the remainder is 0, so 2 is a divisor of 1636)
1636 / 3 = 545.33333333333 (the remainder is 1, so 3 is not a divisor of 1636)
...
1636 / 1635 = 1.0006116207951 (the remainder is 1, so 1635 is not a divisor of 1636)
1636 / 1636 = 1 (the remainder is 0, so 1636 is a divisor of 1636)

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 1636 (i.e. 40.447496832313). 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 $\frac{N}{d} = D$ )

1636 / 1 = 1636 (the remainder is 0, so 1 and 1636 are divisors of 1636)
1636 / 2 = 818 (the remainder is 0, so 2 and 818 are divisors of 1636)
1636 / 3 = 545.33333333333 (the remainder is 1, so 3 is not a divisor of 1636)
...
1636 / 39 = 41.948717948718 (the remainder is 37, so 39 is not a divisor of 1636)
1636 / 40 = 40.9 (the remainder is 36, so 40 is not a divisor of 1636)