What are the divisors of 5059?

1, 5059

There is a total of 2 positive divisors.
The sum of these divisors is 5060.
The arithmetic mean is 2530.

2 odd divisors

1, 5059

How to compute the divisors of 5059?

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 5059 by each of the numbers from 1 to 5059 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)

5059 / 1 = 5059 (the remainder is 0, so 1 is a divisor of 5059)
5059 / 2 = 2529.5 (the remainder is 1, so 2 is not a divisor of 5059)
5059 / 3 = 1686.3333333333 (the remainder is 1, so 3 is not a divisor of 5059)
...
5059 / 5058 = 1.0001977066034 (the remainder is 1, so 5058 is not a divisor of 5059)
5059 / 5059 = 1 (the remainder is 0, so 5059 is a divisor of 5059)

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 5059 (i.e. 71.126647608333). 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 $\frac{N}{d} = D$ )

5059 / 1 = 5059 (the remainder is 0, so 1 and 5059 are divisors of 5059)
5059 / 2 = 2529.5 (the remainder is 1, so 2 is not a divisor of 5059)
5059 / 3 = 1686.3333333333 (the remainder is 1, so 3 is not a divisor of 5059)
...
5059 / 70 = 72.271428571429 (the remainder is 19, so 70 is not a divisor of 5059)
5059 / 71 = 71.253521126761 (the remainder is 18, so 71 is not a divisor of 5059)