What are the divisors of 789?

1, 3, 263, 789

There is a total of 4 positive divisors.
The sum of these divisors is 1056.
The arithmetic mean is 264.

4 odd divisors

1, 3, 263, 789

How to compute the divisors of 789?

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 789 by each of the numbers from 1 to 789 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)

789 / 1 = 789 (the remainder is 0, so 1 is a divisor of 789)
789 / 2 = 394.5 (the remainder is 1, so 2 is not a divisor of 789)
789 / 3 = 263 (the remainder is 0, so 3 is a divisor of 789)
...
789 / 788 = 1.001269035533 (the remainder is 1, so 788 is not a divisor of 789)
789 / 789 = 1 (the remainder is 0, so 789 is a divisor of 789)

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 789 (i.e. 28.089143810376). 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 $\frac{N}{d} = D$ )

789 / 1 = 789 (the remainder is 0, so 1 and 789 are divisors of 789)
789 / 2 = 394.5 (the remainder is 1, so 2 is not a divisor of 789)
789 / 3 = 263 (the remainder is 0, so 3 and 263 are divisors of 789)
...
789 / 27 = 29.222222222222 (the remainder is 6, so 27 is not a divisor of 789)
789 / 28 = 28.178571428571 (the remainder is 5, so 28 is not a divisor of 789)