What are the divisors of 775?

1, 5, 25, 31, 155, 775

There is a total of 6 positive divisors.
The sum of these divisors is 992.
The arithmetic mean is 165.33333333333.

6 odd divisors

1, 5, 25, 31, 155, 775

How to compute the divisors of 775?

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 775 by each of the numbers from 1 to 775 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)

775 / 1 = 775 (the remainder is 0, so 1 is a divisor of 775)
775 / 2 = 387.5 (the remainder is 1, so 2 is not a divisor of 775)
775 / 3 = 258.33333333333 (the remainder is 1, so 3 is not a divisor of 775)
...
775 / 774 = 1.0012919896641 (the remainder is 1, so 774 is not a divisor of 775)
775 / 775 = 1 (the remainder is 0, so 775 is a divisor of 775)

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 775 (i.e. 27.83882181415). 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 $\frac{N}{d} = D$ )

775 / 1 = 775 (the remainder is 0, so 1 and 775 are divisors of 775)
775 / 2 = 387.5 (the remainder is 1, so 2 is not a divisor of 775)
775 / 3 = 258.33333333333 (the remainder is 1, so 3 is not a divisor of 775)
...
775 / 26 = 29.807692307692 (the remainder is 21, so 26 is not a divisor of 775)
775 / 27 = 28.703703703704 (the remainder is 19, so 27 is not a divisor of 775)