What are the divisors of 1858?

1, 2, 929, 1858

There is a total of 4 positive divisors.
The sum of these divisors is 2790.
The arithmetic mean is 697.5.

2 even divisors

2, 1858

2 odd divisors

1, 929

How to compute the divisors of 1858?

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 1858 by each of the numbers from 1 to 1858 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)

1858 / 1 = 1858 (the remainder is 0, so 1 is a divisor of 1858)
1858 / 2 = 929 (the remainder is 0, so 2 is a divisor of 1858)
1858 / 3 = 619.33333333333 (the remainder is 1, so 3 is not a divisor of 1858)
...
1858 / 1857 = 1.0005385029618 (the remainder is 1, so 1857 is not a divisor of 1858)
1858 / 1858 = 1 (the remainder is 0, so 1858 is a divisor of 1858)

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 1858 (i.e. 43.104524124505). 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 $\frac{N}{d} = D$ )

1858 / 1 = 1858 (the remainder is 0, so 1 and 1858 are divisors of 1858)
1858 / 2 = 929 (the remainder is 0, so 2 and 929 are divisors of 1858)
1858 / 3 = 619.33333333333 (the remainder is 1, so 3 is not a divisor of 1858)
...
1858 / 42 = 44.238095238095 (the remainder is 10, so 42 is not a divisor of 1858)
1858 / 43 = 43.209302325581 (the remainder is 9, so 43 is not a divisor of 1858)