What are the divisors of 859?

1, 859

There is a total of 2 positive divisors.
The sum of these divisors is 860.
The arithmetic mean is 430.

2 odd divisors

1, 859

How to compute the divisors of 859?

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 859 by each of the numbers from 1 to 859 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)

859 / 1 = 859 (the remainder is 0, so 1 is a divisor of 859)
859 / 2 = 429.5 (the remainder is 1, so 2 is not a divisor of 859)
859 / 3 = 286.33333333333 (the remainder is 1, so 3 is not a divisor of 859)
...
859 / 858 = 1.0011655011655 (the remainder is 1, so 858 is not a divisor of 859)
859 / 859 = 1 (the remainder is 0, so 859 is a divisor of 859)

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 859 (i.e. 29.308701779506). 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 $\frac{N}{d} = D$ )

859 / 1 = 859 (the remainder is 0, so 1 and 859 are divisors of 859)
859 / 2 = 429.5 (the remainder is 1, so 2 is not a divisor of 859)
859 / 3 = 286.33333333333 (the remainder is 1, so 3 is not a divisor of 859)
...
859 / 28 = 30.678571428571 (the remainder is 19, so 28 is not a divisor of 859)
859 / 29 = 29.620689655172 (the remainder is 18, so 29 is not a divisor of 859)