What are the divisors of 5017?

1, 29, 173, 5017

There is a total of 4 positive divisors.
The sum of these divisors is 5220.
The arithmetic mean is 1305.

4 odd divisors

1, 29, 173, 5017

How to compute the divisors of 5017?

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 5017 by each of the numbers from 1 to 5017 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)

5017 / 1 = 5017 (the remainder is 0, so 1 is a divisor of 5017)
5017 / 2 = 2508.5 (the remainder is 1, so 2 is not a divisor of 5017)
5017 / 3 = 1672.3333333333 (the remainder is 1, so 3 is not a divisor of 5017)
...
5017 / 5016 = 1.0001993620415 (the remainder is 1, so 5016 is not a divisor of 5017)
5017 / 5017 = 1 (the remainder is 0, so 5017 is a divisor of 5017)

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 5017 (i.e. 70.830784267859). 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 $\frac{N}{d} = D$ )

5017 / 1 = 5017 (the remainder is 0, so 1 and 5017 are divisors of 5017)
5017 / 2 = 2508.5 (the remainder is 1, so 2 is not a divisor of 5017)
5017 / 3 = 1672.3333333333 (the remainder is 1, so 3 is not a divisor of 5017)
...
5017 / 69 = 72.710144927536 (the remainder is 49, so 69 is not a divisor of 5017)
5017 / 70 = 71.671428571429 (the remainder is 47, so 70 is not a divisor of 5017)