What are the divisors of 767?

1, 13, 59, 767

There is a total of 4 positive divisors.
The sum of these divisors is 840.
The arithmetic mean is 210.

4 odd divisors

1, 13, 59, 767

How to compute the divisors of 767?

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 767 by each of the numbers from 1 to 767 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)

767 / 1 = 767 (the remainder is 0, so 1 is a divisor of 767)
767 / 2 = 383.5 (the remainder is 1, so 2 is not a divisor of 767)
767 / 3 = 255.66666666667 (the remainder is 2, so 3 is not a divisor of 767)
...
767 / 766 = 1.0013054830287 (the remainder is 1, so 766 is not a divisor of 767)
767 / 767 = 1 (the remainder is 0, so 767 is a divisor of 767)

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 767 (i.e. 27.694764848252). 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 $\frac{N}{d} = D$ )

767 / 1 = 767 (the remainder is 0, so 1 and 767 are divisors of 767)
767 / 2 = 383.5 (the remainder is 1, so 2 is not a divisor of 767)
767 / 3 = 255.66666666667 (the remainder is 2, so 3 is not a divisor of 767)
...
767 / 26 = 29.5 (the remainder is 13, so 26 is not a divisor of 767)
767 / 27 = 28.407407407407 (the remainder is 11, so 27 is not a divisor of 767)