What are the divisors of 5104?

1, 2, 4, 8, 11, 16, 22, 29, 44, 58, 88, 116, 176, 232, 319, 464, 638, 1276, 2552, 5104

There is a total of 20 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 558.

16 even divisors

2, 4, 8, 16, 22, 44, 58, 88, 116, 176, 232, 464, 638, 1276, 2552, 5104

4 odd divisors

1, 11, 29, 319

How to compute the divisors of 5104?

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 5104 by each of the numbers from 1 to 5104 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)

5104 / 1 = 5104 (the remainder is 0, so 1 is a divisor of 5104)
5104 / 2 = 2552 (the remainder is 0, so 2 is a divisor of 5104)
5104 / 3 = 1701.3333333333 (the remainder is 1, so 3 is not a divisor of 5104)
...
5104 / 5103 = 1.0001959631589 (the remainder is 1, so 5103 is not a divisor of 5104)
5104 / 5104 = 1 (the remainder is 0, so 5104 is a divisor of 5104)

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 5104 (i.e. 71.442284397967). 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 $\frac{N}{d} = D$ )

5104 / 1 = 5104 (the remainder is 0, so 1 and 5104 are divisors of 5104)
5104 / 2 = 2552 (the remainder is 0, so 2 and 2552 are divisors of 5104)
5104 / 3 = 1701.3333333333 (the remainder is 1, so 3 is not a divisor of 5104)
...
5104 / 70 = 72.914285714286 (the remainder is 64, so 70 is not a divisor of 5104)
5104 / 71 = 71.887323943662 (the remainder is 63, so 71 is not a divisor of 5104)