What are the divisors of 1826?

1, 2, 11, 22, 83, 166, 913, 1826

There is a total of 8 positive divisors.
The sum of these divisors is 3024.
The arithmetic mean is 378.

4 even divisors

2, 22, 166, 1826

4 odd divisors

1, 11, 83, 913

How to compute the divisors of 1826?

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 1826 by each of the numbers from 1 to 1826 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)

1826 / 1 = 1826 (the remainder is 0, so 1 is a divisor of 1826)
1826 / 2 = 913 (the remainder is 0, so 2 is a divisor of 1826)
1826 / 3 = 608.66666666667 (the remainder is 2, so 3 is not a divisor of 1826)
...
1826 / 1825 = 1.0005479452055 (the remainder is 1, so 1825 is not a divisor of 1826)
1826 / 1826 = 1 (the remainder is 0, so 1826 is a divisor of 1826)

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 1826 (i.e. 42.731721238443). 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 $\frac{N}{d} = D$ )

1826 / 1 = 1826 (the remainder is 0, so 1 and 1826 are divisors of 1826)
1826 / 2 = 913 (the remainder is 0, so 2 and 913 are divisors of 1826)
1826 / 3 = 608.66666666667 (the remainder is 2, so 3 is not a divisor of 1826)
...
1826 / 41 = 44.536585365854 (the remainder is 22, so 41 is not a divisor of 1826)
1826 / 42 = 43.47619047619 (the remainder is 20, so 42 is not a divisor of 1826)