What are the divisors of 1808?

1, 2, 4, 8, 16, 113, 226, 452, 904, 1808

There is a total of 10 positive divisors.
The sum of these divisors is 3534.
The arithmetic mean is 353.4.

8 even divisors

2, 4, 8, 16, 226, 452, 904, 1808

2 odd divisors

1, 113

How to compute the divisors of 1808?

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 1808 by each of the numbers from 1 to 1808 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)

1808 / 1 = 1808 (the remainder is 0, so 1 is a divisor of 1808)
1808 / 2 = 904 (the remainder is 0, so 2 is a divisor of 1808)
1808 / 3 = 602.66666666667 (the remainder is 2, so 3 is not a divisor of 1808)
...
1808 / 1807 = 1.0005534034311 (the remainder is 1, so 1807 is not a divisor of 1808)
1808 / 1808 = 1 (the remainder is 0, so 1808 is a divisor of 1808)

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 1808 (i.e. 42.520583250939). 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 $\frac{N}{d} = D$ )

1808 / 1 = 1808 (the remainder is 0, so 1 and 1808 are divisors of 1808)
1808 / 2 = 904 (the remainder is 0, so 2 and 904 are divisors of 1808)
1808 / 3 = 602.66666666667 (the remainder is 2, so 3 is not a divisor of 1808)
...
1808 / 41 = 44.09756097561 (the remainder is 4, so 41 is not a divisor of 1808)
1808 / 42 = 43.047619047619 (the remainder is 2, so 42 is not a divisor of 1808)