What are the divisors of 5096?

1, 2, 4, 7, 8, 13, 14, 26, 28, 49, 52, 56, 91, 98, 104, 182, 196, 364, 392, 637, 728, 1274, 2548, 5096

There is a total of 24 positive divisors.
The sum of these divisors is 11970.
The arithmetic mean is 498.75.

18 even divisors

2, 4, 8, 14, 26, 28, 52, 56, 98, 104, 182, 196, 364, 392, 728, 1274, 2548, 5096

6 odd divisors

1, 7, 13, 49, 91, 637

How to compute the divisors of 5096?

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 5096 by each of the numbers from 1 to 5096 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)

5096 / 1 = 5096 (the remainder is 0, so 1 is a divisor of 5096)
5096 / 2 = 2548 (the remainder is 0, so 2 is a divisor of 5096)
5096 / 3 = 1698.6666666667 (the remainder is 2, so 3 is not a divisor of 5096)
...
5096 / 5095 = 1.0001962708538 (the remainder is 1, so 5095 is not a divisor of 5096)
5096 / 5096 = 1 (the remainder is 0, so 5096 is a divisor of 5096)

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 5096 (i.e. 71.386273190299). 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 $\frac{N}{d} = D$ )

5096 / 1 = 5096 (the remainder is 0, so 1 and 5096 are divisors of 5096)
5096 / 2 = 2548 (the remainder is 0, so 2 and 2548 are divisors of 5096)
5096 / 3 = 1698.6666666667 (the remainder is 2, so 3 is not a divisor of 5096)
...
5096 / 70 = 72.8 (the remainder is 56, so 70 is not a divisor of 5096)
5096 / 71 = 71.774647887324 (the remainder is 55, so 71 is not a divisor of 5096)