What are the divisors of 1828?

1, 2, 4, 457, 914, 1828

There is a total of 6 positive divisors.
The sum of these divisors is 3206.
The arithmetic mean is 534.33333333333.

4 even divisors

2, 4, 914, 1828

2 odd divisors

1, 457

How to compute the divisors of 1828?

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 1828 by each of the numbers from 1 to 1828 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)

1828 / 1 = 1828 (the remainder is 0, so 1 is a divisor of 1828)
1828 / 2 = 914 (the remainder is 0, so 2 is a divisor of 1828)
1828 / 3 = 609.33333333333 (the remainder is 1, so 3 is not a divisor of 1828)
...
1828 / 1827 = 1.0005473453749 (the remainder is 1, so 1827 is not a divisor of 1828)
1828 / 1828 = 1 (the remainder is 0, so 1828 is a divisor of 1828)

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 1828 (i.e. 42.755116652864). 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 $\frac{N}{d} = D$ )

1828 / 1 = 1828 (the remainder is 0, so 1 and 1828 are divisors of 1828)
1828 / 2 = 914 (the remainder is 0, so 2 and 914 are divisors of 1828)
1828 / 3 = 609.33333333333 (the remainder is 1, so 3 is not a divisor of 1828)
...
1828 / 41 = 44.585365853659 (the remainder is 24, so 41 is not a divisor of 1828)
1828 / 42 = 43.52380952381 (the remainder is 22, so 42 is not a divisor of 1828)