What are the divisors of 886?

1, 2, 443, 886

There is a total of 4 positive divisors.
The sum of these divisors is 1332.
The arithmetic mean is 333.

2 even divisors

2, 886

2 odd divisors

1, 443

How to compute the divisors of 886?

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 886 by each of the numbers from 1 to 886 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)

886 / 1 = 886 (the remainder is 0, so 1 is a divisor of 886)
886 / 2 = 443 (the remainder is 0, so 2 is a divisor of 886)
886 / 3 = 295.33333333333 (the remainder is 1, so 3 is not a divisor of 886)
...
886 / 885 = 1.0011299435028 (the remainder is 1, so 885 is not a divisor of 886)
886 / 886 = 1 (the remainder is 0, so 886 is a divisor of 886)

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 886 (i.e. 29.765752132274). 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 $\frac{N}{d} = D$ )

886 / 1 = 886 (the remainder is 0, so 1 and 886 are divisors of 886)
886 / 2 = 443 (the remainder is 0, so 2 and 443 are divisors of 886)
886 / 3 = 295.33333333333 (the remainder is 1, so 3 is not a divisor of 886)
...
886 / 28 = 31.642857142857 (the remainder is 18, so 28 is not a divisor of 886)
886 / 29 = 30.551724137931 (the remainder is 16, so 29 is not a divisor of 886)