What are the divisors of 5695?

1, 5, 17, 67, 85, 335, 1139, 5695

There is a total of 8 positive divisors.
The sum of these divisors is 7344.
The arithmetic mean is 918.

8 odd divisors

1, 5, 17, 67, 85, 335, 1139, 5695

How to compute the divisors of 5695?

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 5695 by each of the numbers from 1 to 5695 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)

5695 / 1 = 5695 (the remainder is 0, so 1 is a divisor of 5695)
5695 / 2 = 2847.5 (the remainder is 1, so 2 is not a divisor of 5695)
5695 / 3 = 1898.3333333333 (the remainder is 1, so 3 is not a divisor of 5695)
...
5695 / 5694 = 1.0001756234633 (the remainder is 1, so 5694 is not a divisor of 5695)
5695 / 5695 = 1 (the remainder is 0, so 5695 is a divisor of 5695)

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 5695 (i.e. 75.465223778904). 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 $\frac{N}{d} = D$ )

5695 / 1 = 5695 (the remainder is 0, so 1 and 5695 are divisors of 5695)
5695 / 2 = 2847.5 (the remainder is 1, so 2 is not a divisor of 5695)
5695 / 3 = 1898.3333333333 (the remainder is 1, so 3 is not a divisor of 5695)
...
5695 / 74 = 76.959459459459 (the remainder is 71, so 74 is not a divisor of 5695)
5695 / 75 = 75.933333333333 (the remainder is 70, so 75 is not a divisor of 5695)