What are the divisors of 871?

1, 13, 67, 871

There is a total of 4 positive divisors.
The sum of these divisors is 952.
The arithmetic mean is 238.

4 odd divisors

1, 13, 67, 871

How to compute the divisors of 871?

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 871 by each of the numbers from 1 to 871 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)

871 / 1 = 871 (the remainder is 0, so 1 is a divisor of 871)
871 / 2 = 435.5 (the remainder is 1, so 2 is not a divisor of 871)
871 / 3 = 290.33333333333 (the remainder is 1, so 3 is not a divisor of 871)
...
871 / 870 = 1.0011494252874 (the remainder is 1, so 870 is not a divisor of 871)
871 / 871 = 1 (the remainder is 0, so 871 is a divisor of 871)

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 871 (i.e. 29.512709126747). 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 $\frac{N}{d} = D$ )

871 / 1 = 871 (the remainder is 0, so 1 and 871 are divisors of 871)
871 / 2 = 435.5 (the remainder is 1, so 2 is not a divisor of 871)
871 / 3 = 290.33333333333 (the remainder is 1, so 3 is not a divisor of 871)
...
871 / 28 = 31.107142857143 (the remainder is 3, so 28 is not a divisor of 871)
871 / 29 = 30.034482758621 (the remainder is 1, so 29 is not a divisor of 871)