What are the divisors of 787?

1, 787

There is a total of 2 positive divisors.
The sum of these divisors is 788.
The arithmetic mean is 394.

2 odd divisors

1, 787

How to compute the divisors of 787?

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 787 by each of the numbers from 1 to 787 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)

787 / 1 = 787 (the remainder is 0, so 1 is a divisor of 787)
787 / 2 = 393.5 (the remainder is 1, so 2 is not a divisor of 787)
787 / 3 = 262.33333333333 (the remainder is 1, so 3 is not a divisor of 787)
...
787 / 786 = 1.001272264631 (the remainder is 1, so 786 is not a divisor of 787)
787 / 787 = 1 (the remainder is 0, so 787 is a divisor of 787)

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 787 (i.e. 28.053520278211). 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 $\frac{N}{d} = D$ )

787 / 1 = 787 (the remainder is 0, so 1 and 787 are divisors of 787)
787 / 2 = 393.5 (the remainder is 1, so 2 is not a divisor of 787)
787 / 3 = 262.33333333333 (the remainder is 1, so 3 is not a divisor of 787)
...
787 / 27 = 29.148148148148 (the remainder is 4, so 27 is not a divisor of 787)
787 / 28 = 28.107142857143 (the remainder is 3, so 28 is not a divisor of 787)