What are the divisors of 856?

1, 2, 4, 8, 107, 214, 428, 856

There is a total of 8 positive divisors.
The sum of these divisors is 1620.
The arithmetic mean is 202.5.

6 even divisors

2, 4, 8, 214, 428, 856

2 odd divisors

1, 107

How to compute the divisors of 856?

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 856 by each of the numbers from 1 to 856 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)

856 / 1 = 856 (the remainder is 0, so 1 is a divisor of 856)
856 / 2 = 428 (the remainder is 0, so 2 is a divisor of 856)
856 / 3 = 285.33333333333 (the remainder is 1, so 3 is not a divisor of 856)
...
856 / 855 = 1.0011695906433 (the remainder is 1, so 855 is not a divisor of 856)
856 / 856 = 1 (the remainder is 0, so 856 is a divisor of 856)

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 856 (i.e. 29.257477676656). 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 $\frac{N}{d} = D$ )

856 / 1 = 856 (the remainder is 0, so 1 and 856 are divisors of 856)
856 / 2 = 428 (the remainder is 0, so 2 and 428 are divisors of 856)
856 / 3 = 285.33333333333 (the remainder is 1, so 3 is not a divisor of 856)
...
856 / 28 = 30.571428571429 (the remainder is 16, so 28 is not a divisor of 856)
856 / 29 = 29.51724137931 (the remainder is 15, so 29 is not a divisor of 856)