What are the divisors of 5368?

1, 2, 4, 8, 11, 22, 44, 61, 88, 122, 244, 488, 671, 1342, 2684, 5368

There is a total of 16 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 697.5.

12 even divisors

2, 4, 8, 22, 44, 88, 122, 244, 488, 1342, 2684, 5368

4 odd divisors

1, 11, 61, 671

How to compute the divisors of 5368?

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 5368 by each of the numbers from 1 to 5368 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)

5368 / 1 = 5368 (the remainder is 0, so 1 is a divisor of 5368)
5368 / 2 = 2684 (the remainder is 0, so 2 is a divisor of 5368)
5368 / 3 = 1789.3333333333 (the remainder is 1, so 3 is not a divisor of 5368)
...
5368 / 5367 = 1.0001863238308 (the remainder is 1, so 5367 is not a divisor of 5368)
5368 / 5368 = 1 (the remainder is 0, so 5368 is a divisor of 5368)

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 5368 (i.e. 73.266636336057). 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 $\frac{N}{d} = D$ )

5368 / 1 = 5368 (the remainder is 0, so 1 and 5368 are divisors of 5368)
5368 / 2 = 2684 (the remainder is 0, so 2 and 2684 are divisors of 5368)
5368 / 3 = 1789.3333333333 (the remainder is 1, so 3 is not a divisor of 5368)
...
5368 / 72 = 74.555555555556 (the remainder is 40, so 72 is not a divisor of 5368)
5368 / 73 = 73.534246575342 (the remainder is 39, so 73 is not a divisor of 5368)