What are the divisors of 796?

1, 2, 4, 199, 398, 796

There is a total of 6 positive divisors.
The sum of these divisors is 1400.
The arithmetic mean is 233.33333333333.

4 even divisors

2, 4, 398, 796

2 odd divisors

1, 199

How to compute the divisors of 796?

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 796 by each of the numbers from 1 to 796 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)

796 / 1 = 796 (the remainder is 0, so 1 is a divisor of 796)
796 / 2 = 398 (the remainder is 0, so 2 is a divisor of 796)
796 / 3 = 265.33333333333 (the remainder is 1, so 3 is not a divisor of 796)
...
796 / 795 = 1.0012578616352 (the remainder is 1, so 795 is not a divisor of 796)
796 / 796 = 1 (the remainder is 0, so 796 is a divisor of 796)

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 796 (i.e. 28.213471959332). 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 $\frac{N}{d} = D$ )

796 / 1 = 796 (the remainder is 0, so 1 and 796 are divisors of 796)
796 / 2 = 398 (the remainder is 0, so 2 and 398 are divisors of 796)
796 / 3 = 265.33333333333 (the remainder is 1, so 3 is not a divisor of 796)
...
796 / 27 = 29.481481481481 (the remainder is 13, so 27 is not a divisor of 796)
796 / 28 = 28.428571428571 (the remainder is 12, so 28 is not a divisor of 796)