What are the divisors of 5366?

1, 2, 2683, 5366

There is a total of 4 positive divisors.
The sum of these divisors is 8052.
The arithmetic mean is 2013.

2 even divisors

2, 5366

2 odd divisors

1, 2683

How to compute the divisors of 5366?

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 5366 by each of the numbers from 1 to 5366 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)

5366 / 1 = 5366 (the remainder is 0, so 1 is a divisor of 5366)
5366 / 2 = 2683 (the remainder is 0, so 2 is a divisor of 5366)
5366 / 3 = 1788.6666666667 (the remainder is 2, so 3 is not a divisor of 5366)
...
5366 / 5365 = 1.0001863932898 (the remainder is 1, so 5365 is not a divisor of 5366)
5366 / 5366 = 1 (the remainder is 0, so 5366 is a divisor of 5366)

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 5366 (i.e. 73.25298628725). 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 $\frac{N}{d} = D$ )

5366 / 1 = 5366 (the remainder is 0, so 1 and 5366 are divisors of 5366)
5366 / 2 = 2683 (the remainder is 0, so 2 and 2683 are divisors of 5366)
5366 / 3 = 1788.6666666667 (the remainder is 2, so 3 is not a divisor of 5366)
...
5366 / 72 = 74.527777777778 (the remainder is 38, so 72 is not a divisor of 5366)
5366 / 73 = 73.506849315068 (the remainder is 37, so 73 is not a divisor of 5366)