What are the divisors of 5117?

1, 7, 17, 43, 119, 301, 731, 5117

There is a total of 8 positive divisors.
The sum of these divisors is 6336.
The arithmetic mean is 792.

8 odd divisors

1, 7, 17, 43, 119, 301, 731, 5117

How to compute the divisors of 5117?

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 5117 by each of the numbers from 1 to 5117 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)

5117 / 1 = 5117 (the remainder is 0, so 1 is a divisor of 5117)
5117 / 2 = 2558.5 (the remainder is 1, so 2 is not a divisor of 5117)
5117 / 3 = 1705.6666666667 (the remainder is 2, so 3 is not a divisor of 5117)
...
5117 / 5116 = 1.0001954652072 (the remainder is 1, so 5116 is not a divisor of 5117)
5117 / 5117 = 1 (the remainder is 0, so 5117 is a divisor of 5117)

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 5117 (i.e. 71.533209071032). 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 $\frac{N}{d} = D$ )

5117 / 1 = 5117 (the remainder is 0, so 1 and 5117 are divisors of 5117)
5117 / 2 = 2558.5 (the remainder is 1, so 2 is not a divisor of 5117)
5117 / 3 = 1705.6666666667 (the remainder is 2, so 3 is not a divisor of 5117)
...
5117 / 70 = 73.1 (the remainder is 7, so 70 is not a divisor of 5117)
5117 / 71 = 72.070422535211 (the remainder is 5, so 71 is not a divisor of 5117)