What are the divisors of 812?

1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812

There is a total of 12 positive divisors.
The sum of these divisors is 1680.
The arithmetic mean is 140.

8 even divisors

2, 4, 14, 28, 58, 116, 406, 812

4 odd divisors

1, 7, 29, 203

How to compute the divisors of 812?

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 812 by each of the numbers from 1 to 812 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)

812 / 1 = 812 (the remainder is 0, so 1 is a divisor of 812)
812 / 2 = 406 (the remainder is 0, so 2 is a divisor of 812)
812 / 3 = 270.66666666667 (the remainder is 2, so 3 is not a divisor of 812)
...
812 / 811 = 1.0012330456227 (the remainder is 1, so 811 is not a divisor of 812)
812 / 812 = 1 (the remainder is 0, so 812 is a divisor of 812)

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 812 (i.e. 28.49561369755). 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 $\frac{N}{d} = D$ )

812 / 1 = 812 (the remainder is 0, so 1 and 812 are divisors of 812)
812 / 2 = 406 (the remainder is 0, so 2 and 406 are divisors of 812)
812 / 3 = 270.66666666667 (the remainder is 2, so 3 is not a divisor of 812)
...
812 / 27 = 30.074074074074 (the remainder is 2, so 27 is not a divisor of 812)
812 / 28 = 29 (the remainder is 0, so 28 and 29 are divisors of 812)