What are the divisors of 5068?

1, 2, 4, 7, 14, 28, 181, 362, 724, 1267, 2534, 5068

There is a total of 12 positive divisors.
The sum of these divisors is 10192.
The arithmetic mean is 849.33333333333.

8 even divisors

2, 4, 14, 28, 362, 724, 2534, 5068

4 odd divisors

1, 7, 181, 1267

How to compute the divisors of 5068?

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 5068 by each of the numbers from 1 to 5068 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)

5068 / 1 = 5068 (the remainder is 0, so 1 is a divisor of 5068)
5068 / 2 = 2534 (the remainder is 0, so 2 is a divisor of 5068)
5068 / 3 = 1689.3333333333 (the remainder is 1, so 3 is not a divisor of 5068)
...
5068 / 5067 = 1.0001973554371 (the remainder is 1, so 5067 is not a divisor of 5068)
5068 / 5068 = 1 (the remainder is 0, so 5068 is a divisor of 5068)

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 5068 (i.e. 71.189886922231). 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 $\frac{N}{d} = D$ )

5068 / 1 = 5068 (the remainder is 0, so 1 and 5068 are divisors of 5068)
5068 / 2 = 2534 (the remainder is 0, so 2 and 2534 are divisors of 5068)
5068 / 3 = 1689.3333333333 (the remainder is 1, so 3 is not a divisor of 5068)
...
5068 / 70 = 72.4 (the remainder is 28, so 70 is not a divisor of 5068)
5068 / 71 = 71.380281690141 (the remainder is 27, so 71 is not a divisor of 5068)