What are the divisors of 1816?

1, 2, 4, 8, 227, 454, 908, 1816

There is a total of 8 positive divisors.
The sum of these divisors is 3420.
The arithmetic mean is 427.5.

6 even divisors

2, 4, 8, 454, 908, 1816

2 odd divisors

1, 227

How to compute the divisors of 1816?

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 1816 by each of the numbers from 1 to 1816 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)

1816 / 1 = 1816 (the remainder is 0, so 1 is a divisor of 1816)
1816 / 2 = 908 (the remainder is 0, so 2 is a divisor of 1816)
1816 / 3 = 605.33333333333 (the remainder is 1, so 3 is not a divisor of 1816)
...
1816 / 1815 = 1.0005509641873 (the remainder is 1, so 1815 is not a divisor of 1816)
1816 / 1816 = 1 (the remainder is 0, so 1816 is a divisor of 1816)

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 1816 (i.e. 42.614551505325). 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 $\frac{N}{d} = D$ )

1816 / 1 = 1816 (the remainder is 0, so 1 and 1816 are divisors of 1816)
1816 / 2 = 908 (the remainder is 0, so 2 and 908 are divisors of 1816)
1816 / 3 = 605.33333333333 (the remainder is 1, so 3 is not a divisor of 1816)
...
1816 / 41 = 44.292682926829 (the remainder is 12, so 41 is not a divisor of 1816)
1816 / 42 = 43.238095238095 (the remainder is 10, so 42 is not a divisor of 1816)