What are the divisors of 5116?

1, 2, 4, 1279, 2558, 5116

There is a total of 6 positive divisors.
The sum of these divisors is 8960.
The arithmetic mean is 1493.3333333333.

4 even divisors

2, 4, 2558, 5116

2 odd divisors

1, 1279

How to compute the divisors of 5116?

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 5116 by each of the numbers from 1 to 5116 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)

5116 / 1 = 5116 (the remainder is 0, so 1 is a divisor of 5116)
5116 / 2 = 2558 (the remainder is 0, so 2 is a divisor of 5116)
5116 / 3 = 1705.3333333333 (the remainder is 1, so 3 is not a divisor of 5116)
...
5116 / 5115 = 1.0001955034213 (the remainder is 1, so 5115 is not a divisor of 5116)
5116 / 5116 = 1 (the remainder is 0, so 5116 is a divisor of 5116)

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 5116 (i.e. 71.526218968991). 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 $\frac{N}{d} = D$ )

5116 / 1 = 5116 (the remainder is 0, so 1 and 5116 are divisors of 5116)
5116 / 2 = 2558 (the remainder is 0, so 2 and 2558 are divisors of 5116)
5116 / 3 = 1705.3333333333 (the remainder is 1, so 3 is not a divisor of 5116)
...
5116 / 70 = 73.085714285714 (the remainder is 6, so 70 is not a divisor of 5116)
5116 / 71 = 72.056338028169 (the remainder is 4, so 71 is not a divisor of 5116)