What are the divisors of 858?

1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858

There is a total of 16 positive divisors.
The sum of these divisors is 2016.
The arithmetic mean is 126.

8 even divisors

2, 6, 22, 26, 66, 78, 286, 858

8 odd divisors

1, 3, 11, 13, 33, 39, 143, 429

How to compute the divisors of 858?

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 858 by each of the numbers from 1 to 858 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)

858 / 1 = 858 (the remainder is 0, so 1 is a divisor of 858)
858 / 2 = 429 (the remainder is 0, so 2 is a divisor of 858)
858 / 3 = 286 (the remainder is 0, so 3 is a divisor of 858)
...
858 / 857 = 1.0011668611435 (the remainder is 1, so 857 is not a divisor of 858)
858 / 858 = 1 (the remainder is 0, so 858 is a divisor of 858)

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 858 (i.e. 29.291637031754). 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 $\frac{N}{d} = D$ )

858 / 1 = 858 (the remainder is 0, so 1 and 858 are divisors of 858)
858 / 2 = 429 (the remainder is 0, so 2 and 429 are divisors of 858)
858 / 3 = 286 (the remainder is 0, so 3 and 286 are divisors of 858)
...
858 / 28 = 30.642857142857 (the remainder is 18, so 28 is not a divisor of 858)
858 / 29 = 29.586206896552 (the remainder is 17, so 29 is not a divisor of 858)