What are the divisors of 862?

1, 2, 431, 862

There is a total of 4 positive divisors.
The sum of these divisors is 1296.
The arithmetic mean is 324.

2 even divisors

2, 862

2 odd divisors

1, 431

How to compute the divisors of 862?

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 862 by each of the numbers from 1 to 862 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)

862 / 1 = 862 (the remainder is 0, so 1 is a divisor of 862)
862 / 2 = 431 (the remainder is 0, so 2 is a divisor of 862)
862 / 3 = 287.33333333333 (the remainder is 1, so 3 is not a divisor of 862)
...
862 / 861 = 1.0011614401858 (the remainder is 1, so 861 is not a divisor of 862)
862 / 862 = 1 (the remainder is 0, so 862 is a divisor of 862)

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 862 (i.e. 29.359836511806). 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 $\frac{N}{d} = D$ )

862 / 1 = 862 (the remainder is 0, so 1 and 862 are divisors of 862)
862 / 2 = 431 (the remainder is 0, so 2 and 431 are divisors of 862)
862 / 3 = 287.33333333333 (the remainder is 1, so 3 is not a divisor of 862)
...
862 / 28 = 30.785714285714 (the remainder is 22, so 28 is not a divisor of 862)
862 / 29 = 29.724137931034 (the remainder is 21, so 29 is not a divisor of 862)