What are the divisors of 1846?

1, 2, 13, 26, 71, 142, 923, 1846

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

4 even divisors

2, 26, 142, 1846

4 odd divisors

1, 13, 71, 923

How to compute the divisors of 1846?

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 1846 by each of the numbers from 1 to 1846 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)

1846 / 1 = 1846 (the remainder is 0, so 1 is a divisor of 1846)
1846 / 2 = 923 (the remainder is 0, so 2 is a divisor of 1846)
1846 / 3 = 615.33333333333 (the remainder is 1, so 3 is not a divisor of 1846)
...
1846 / 1845 = 1.0005420054201 (the remainder is 1, so 1845 is not a divisor of 1846)
1846 / 1846 = 1 (the remainder is 0, so 1846 is a divisor of 1846)

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 1846 (i.e. 42.965102117882). 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 $\frac{N}{d} = D$ )

1846 / 1 = 1846 (the remainder is 0, so 1 and 1846 are divisors of 1846)
1846 / 2 = 923 (the remainder is 0, so 2 and 923 are divisors of 1846)
1846 / 3 = 615.33333333333 (the remainder is 1, so 3 is not a divisor of 1846)
...
1846 / 41 = 45.024390243902 (the remainder is 1, so 41 is not a divisor of 1846)
1846 / 42 = 43.952380952381 (the remainder is 40, so 42 is not a divisor of 1846)