What are the divisors of 5286?

1, 2, 3, 6, 881, 1762, 2643, 5286

There is a total of 8 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 1323.

4 even divisors

2, 6, 1762, 5286

4 odd divisors

1, 3, 881, 2643

How to compute the divisors of 5286?

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 5286 by each of the numbers from 1 to 5286 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)

5286 / 1 = 5286 (the remainder is 0, so 1 is a divisor of 5286)
5286 / 2 = 2643 (the remainder is 0, so 2 is a divisor of 5286)
5286 / 3 = 1762 (the remainder is 0, so 3 is a divisor of 5286)
...
5286 / 5285 = 1.0001892147588 (the remainder is 1, so 5285 is not a divisor of 5286)
5286 / 5286 = 1 (the remainder is 0, so 5286 is a divisor of 5286)

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 5286 (i.e. 72.704882917174). 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 $\frac{N}{d} = D$ )

5286 / 1 = 5286 (the remainder is 0, so 1 and 5286 are divisors of 5286)
5286 / 2 = 2643 (the remainder is 0, so 2 and 2643 are divisors of 5286)
5286 / 3 = 1762 (the remainder is 0, so 3 and 1762 are divisors of 5286)
...
5286 / 71 = 74.450704225352 (the remainder is 32, so 71 is not a divisor of 5286)
5286 / 72 = 73.416666666667 (the remainder is 30, so 72 is not a divisor of 5286)