What are the divisors of 793?

1, 13, 61, 793

There is a total of 4 positive divisors.
The sum of these divisors is 868.
The arithmetic mean is 217.

4 odd divisors

1, 13, 61, 793

How to compute the divisors of 793?

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 793 by each of the numbers from 1 to 793 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)

793 / 1 = 793 (the remainder is 0, so 1 is a divisor of 793)
793 / 2 = 396.5 (the remainder is 1, so 2 is not a divisor of 793)
793 / 3 = 264.33333333333 (the remainder is 1, so 3 is not a divisor of 793)
...
793 / 792 = 1.0012626262626 (the remainder is 1, so 792 is not a divisor of 793)
793 / 793 = 1 (the remainder is 0, so 793 is a divisor of 793)

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 793 (i.e. 28.160255680657). 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 $\frac{N}{d} = D$ )

793 / 1 = 793 (the remainder is 0, so 1 and 793 are divisors of 793)
793 / 2 = 396.5 (the remainder is 1, so 2 is not a divisor of 793)
793 / 3 = 264.33333333333 (the remainder is 1, so 3 is not a divisor of 793)
...
793 / 27 = 29.37037037037 (the remainder is 10, so 27 is not a divisor of 793)
793 / 28 = 28.321428571429 (the remainder is 9, so 28 is not a divisor of 793)