What are the divisors of 766?

1, 2, 383, 766

There is a total of 4 positive divisors.
The sum of these divisors is 1152.
The arithmetic mean is 288.

2 even divisors

2, 766

2 odd divisors

1, 383

How to compute the divisors of 766?

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 766 by each of the numbers from 1 to 766 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)

766 / 1 = 766 (the remainder is 0, so 1 is a divisor of 766)
766 / 2 = 383 (the remainder is 0, so 2 is a divisor of 766)
766 / 3 = 255.33333333333 (the remainder is 1, so 3 is not a divisor of 766)
...
766 / 765 = 1.0013071895425 (the remainder is 1, so 765 is not a divisor of 766)
766 / 766 = 1 (the remainder is 0, so 766 is a divisor of 766)

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 766 (i.e. 27.676705006196). 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 $\frac{N}{d} = D$ )

766 / 1 = 766 (the remainder is 0, so 1 and 766 are divisors of 766)
766 / 2 = 383 (the remainder is 0, so 2 and 383 are divisors of 766)
766 / 3 = 255.33333333333 (the remainder is 1, so 3 is not a divisor of 766)
...
766 / 26 = 29.461538461538 (the remainder is 12, so 26 is not a divisor of 766)
766 / 27 = 28.37037037037 (the remainder is 10, so 27 is not a divisor of 766)