What are the divisors of 5060?

1, 2, 4, 5, 10, 11, 20, 22, 23, 44, 46, 55, 92, 110, 115, 220, 230, 253, 460, 506, 1012, 1265, 2530, 5060

There is a total of 24 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 504.

16 even divisors

2, 4, 10, 20, 22, 44, 46, 92, 110, 220, 230, 460, 506, 1012, 2530, 5060

8 odd divisors

1, 5, 11, 23, 55, 115, 253, 1265

How to compute the divisors of 5060?

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 5060 by each of the numbers from 1 to 5060 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)

5060 / 1 = 5060 (the remainder is 0, so 1 is a divisor of 5060)
5060 / 2 = 2530 (the remainder is 0, so 2 is a divisor of 5060)
5060 / 3 = 1686.6666666667 (the remainder is 2, so 3 is not a divisor of 5060)
...
5060 / 5059 = 1.0001976675232 (the remainder is 1, so 5059 is not a divisor of 5060)
5060 / 5060 = 1 (the remainder is 0, so 5060 is a divisor of 5060)

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 5060 (i.e. 71.133676975115). 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 $\frac{N}{d} = D$ )

5060 / 1 = 5060 (the remainder is 0, so 1 and 5060 are divisors of 5060)
5060 / 2 = 2530 (the remainder is 0, so 2 and 2530 are divisors of 5060)
5060 / 3 = 1686.6666666667 (the remainder is 2, so 3 is not a divisor of 5060)
...
5060 / 70 = 72.285714285714 (the remainder is 20, so 70 is not a divisor of 5060)
5060 / 71 = 71.267605633803 (the remainder is 19, so 71 is not a divisor of 5060)