What are the divisors of 887?

1, 887

There is a total of 2 positive divisors.
The sum of these divisors is 888.
The arithmetic mean is 444.

2 odd divisors

1, 887

How to compute the divisors of 887?

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 887 by each of the numbers from 1 to 887 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)

887 / 1 = 887 (the remainder is 0, so 1 is a divisor of 887)
887 / 2 = 443.5 (the remainder is 1, so 2 is not a divisor of 887)
887 / 3 = 295.66666666667 (the remainder is 2, so 3 is not a divisor of 887)
...
887 / 886 = 1.0011286681716 (the remainder is 1, so 886 is not a divisor of 887)
887 / 887 = 1 (the remainder is 0, so 887 is a divisor of 887)

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 887 (i.e. 29.782545223671). 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 $\frac{N}{d} = D$ )

887 / 1 = 887 (the remainder is 0, so 1 and 887 are divisors of 887)
887 / 2 = 443.5 (the remainder is 1, so 2 is not a divisor of 887)
887 / 3 = 295.66666666667 (the remainder is 2, so 3 is not a divisor of 887)
...
887 / 28 = 31.678571428571 (the remainder is 19, so 28 is not a divisor of 887)
887 / 29 = 30.586206896552 (the remainder is 17, so 29 is not a divisor of 887)