What are the divisors of 1822?

1, 2, 911, 1822

There is a total of 4 positive divisors.
The sum of these divisors is 2736.
The arithmetic mean is 684.

2 even divisors

2, 1822

2 odd divisors

1, 911

How to compute the divisors of 1822?

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 1822 by each of the numbers from 1 to 1822 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)

1822 / 1 = 1822 (the remainder is 0, so 1 is a divisor of 1822)
1822 / 2 = 911 (the remainder is 0, so 2 is a divisor of 1822)
1822 / 3 = 607.33333333333 (the remainder is 1, so 3 is not a divisor of 1822)
...
1822 / 1821 = 1.0005491488193 (the remainder is 1, so 1821 is not a divisor of 1822)
1822 / 1822 = 1 (the remainder is 0, so 1822 is a divisor of 1822)

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 1822 (i.e. 42.684891940826). 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 $\frac{N}{d} = D$ )

1822 / 1 = 1822 (the remainder is 0, so 1 and 1822 are divisors of 1822)
1822 / 2 = 911 (the remainder is 0, so 2 and 911 are divisors of 1822)
1822 / 3 = 607.33333333333 (the remainder is 1, so 3 is not a divisor of 1822)
...
1822 / 41 = 44.439024390244 (the remainder is 18, so 41 is not a divisor of 1822)
1822 / 42 = 43.380952380952 (the remainder is 16, so 42 is not a divisor of 1822)