What are the divisors of 5705?

1, 5, 7, 35, 163, 815, 1141, 5705

There is a total of 8 positive divisors.
The sum of these divisors is 7872.
The arithmetic mean is 984.

8 odd divisors

1, 5, 7, 35, 163, 815, 1141, 5705

How to compute the divisors of 5705?

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 5705 by each of the numbers from 1 to 5705 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)

5705 / 1 = 5705 (the remainder is 0, so 1 is a divisor of 5705)
5705 / 2 = 2852.5 (the remainder is 1, so 2 is not a divisor of 5705)
5705 / 3 = 1901.6666666667 (the remainder is 2, so 3 is not a divisor of 5705)
...
5705 / 5704 = 1.000175315568 (the remainder is 1, so 5704 is not a divisor of 5705)
5705 / 5705 = 1 (the remainder is 0, so 5705 is a divisor of 5705)

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 5705 (i.e. 75.531450403127). 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 $\frac{N}{d} = D$ )

5705 / 1 = 5705 (the remainder is 0, so 1 and 5705 are divisors of 5705)
5705 / 2 = 2852.5 (the remainder is 1, so 2 is not a divisor of 5705)
5705 / 3 = 1901.6666666667 (the remainder is 2, so 3 is not a divisor of 5705)
...
5705 / 74 = 77.094594594595 (the remainder is 7, so 74 is not a divisor of 5705)
5705 / 75 = 76.066666666667 (the remainder is 5, so 75 is not a divisor of 5705)