What are the divisors of 794?

1, 2, 397, 794

There is a total of 4 positive divisors.
The sum of these divisors is 1194.
The arithmetic mean is 298.5.

2 even divisors

2, 794

2 odd divisors

1, 397

How to compute the divisors of 794?

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 794 by each of the numbers from 1 to 794 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)

794 / 1 = 794 (the remainder is 0, so 1 is a divisor of 794)
794 / 2 = 397 (the remainder is 0, so 2 is a divisor of 794)
794 / 3 = 264.66666666667 (the remainder is 2, so 3 is not a divisor of 794)
...
794 / 793 = 1.0012610340479 (the remainder is 1, so 793 is not a divisor of 794)
794 / 794 = 1 (the remainder is 0, so 794 is a divisor of 794)

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 794 (i.e. 28.178005607211). 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 $\frac{N}{d} = D$ )

794 / 1 = 794 (the remainder is 0, so 1 and 794 are divisors of 794)
794 / 2 = 397 (the remainder is 0, so 2 and 397 are divisors of 794)
794 / 3 = 264.66666666667 (the remainder is 2, so 3 is not a divisor of 794)
...
794 / 27 = 29.407407407407 (the remainder is 11, so 27 is not a divisor of 794)
794 / 28 = 28.357142857143 (the remainder is 10, so 28 is not a divisor of 794)