What are the divisors of 832?

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832

There is a total of 14 positive divisors.
The sum of these divisors is 1778.
The arithmetic mean is 127.

12 even divisors

2, 4, 8, 16, 26, 32, 52, 64, 104, 208, 416, 832

2 odd divisors

1, 13

How to compute the divisors of 832?

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 832 by each of the numbers from 1 to 832 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)

832 / 1 = 832 (the remainder is 0, so 1 is a divisor of 832)
832 / 2 = 416 (the remainder is 0, so 2 is a divisor of 832)
832 / 3 = 277.33333333333 (the remainder is 1, so 3 is not a divisor of 832)
...
832 / 831 = 1.0012033694344 (the remainder is 1, so 831 is not a divisor of 832)
832 / 832 = 1 (the remainder is 0, so 832 is a divisor of 832)

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 832 (i.e. 28.844410203712). 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 $\frac{N}{d} = D$ )

832 / 1 = 832 (the remainder is 0, so 1 and 832 are divisors of 832)
832 / 2 = 416 (the remainder is 0, so 2 and 416 are divisors of 832)
832 / 3 = 277.33333333333 (the remainder is 1, so 3 is not a divisor of 832)
...
832 / 27 = 30.814814814815 (the remainder is 22, so 27 is not a divisor of 832)
832 / 28 = 29.714285714286 (the remainder is 20, so 28 is not a divisor of 832)