What are the divisors of 5287?

1, 17, 311, 5287

There is a total of 4 positive divisors.
The sum of these divisors is 5616.
The arithmetic mean is 1404.

4 odd divisors

1, 17, 311, 5287

How to compute the divisors of 5287?

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 5287 by each of the numbers from 1 to 5287 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)

5287 / 1 = 5287 (the remainder is 0, so 1 is a divisor of 5287)
5287 / 2 = 2643.5 (the remainder is 1, so 2 is not a divisor of 5287)
5287 / 3 = 1762.3333333333 (the remainder is 1, so 3 is not a divisor of 5287)
...
5287 / 5286 = 1.0001891789633 (the remainder is 1, so 5286 is not a divisor of 5287)
5287 / 5287 = 1 (the remainder is 0, so 5287 is a divisor of 5287)

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 5287 (i.e. 72.711759709142). 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 $\frac{N}{d} = D$ )

5287 / 1 = 5287 (the remainder is 0, so 1 and 5287 are divisors of 5287)
5287 / 2 = 2643.5 (the remainder is 1, so 2 is not a divisor of 5287)
5287 / 3 = 1762.3333333333 (the remainder is 1, so 3 is not a divisor of 5287)
...
5287 / 71 = 74.464788732394 (the remainder is 33, so 71 is not a divisor of 5287)
5287 / 72 = 73.430555555556 (the remainder is 31, so 72 is not a divisor of 5287)