What are the divisors of 863?

1, 863

There is a total of 2 positive divisors.
The sum of these divisors is 864.
The arithmetic mean is 432.

2 odd divisors

1, 863

How to compute the divisors of 863?

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 863 by each of the numbers from 1 to 863 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)

863 / 1 = 863 (the remainder is 0, so 1 is a divisor of 863)
863 / 2 = 431.5 (the remainder is 1, so 2 is not a divisor of 863)
863 / 3 = 287.66666666667 (the remainder is 2, so 3 is not a divisor of 863)
...
863 / 862 = 1.0011600928074 (the remainder is 1, so 862 is not a divisor of 863)
863 / 863 = 1 (the remainder is 0, so 863 is a divisor of 863)

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 863 (i.e. 29.376861643137). 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 $\frac{N}{d} = D$ )

863 / 1 = 863 (the remainder is 0, so 1 and 863 are divisors of 863)
863 / 2 = 431.5 (the remainder is 1, so 2 is not a divisor of 863)
863 / 3 = 287.66666666667 (the remainder is 2, so 3 is not a divisor of 863)
...
863 / 28 = 30.821428571429 (the remainder is 23, so 28 is not a divisor of 863)
863 / 29 = 29.758620689655 (the remainder is 22, so 29 is not a divisor of 863)