What are the divisors of 788?

1, 2, 4, 197, 394, 788

There is a total of 6 positive divisors.
The sum of these divisors is 1386.
The arithmetic mean is 231.

4 even divisors

2, 4, 394, 788

2 odd divisors

1, 197

How to compute the divisors of 788?

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 788 by each of the numbers from 1 to 788 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)

788 / 1 = 788 (the remainder is 0, so 1 is a divisor of 788)
788 / 2 = 394 (the remainder is 0, so 2 is a divisor of 788)
788 / 3 = 262.66666666667 (the remainder is 2, so 3 is not a divisor of 788)
...
788 / 787 = 1.0012706480305 (the remainder is 1, so 787 is not a divisor of 788)
788 / 788 = 1 (the remainder is 0, so 788 is a divisor of 788)

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 788 (i.e. 28.071337695236). 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 $\frac{N}{d} = D$ )

788 / 1 = 788 (the remainder is 0, so 1 and 788 are divisors of 788)
788 / 2 = 394 (the remainder is 0, so 2 and 394 are divisors of 788)
788 / 3 = 262.66666666667 (the remainder is 2, so 3 is not a divisor of 788)
...
788 / 27 = 29.185185185185 (the remainder is 5, so 27 is not a divisor of 788)
788 / 28 = 28.142857142857 (the remainder is 4, so 28 is not a divisor of 788)