What are the divisors of 5087?

1, 5087

There is a total of 2 positive divisors.
The sum of these divisors is 5088.
The arithmetic mean is 2544.

2 odd divisors

1, 5087

How to compute the divisors of 5087?

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 5087 by each of the numbers from 1 to 5087 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)

5087 / 1 = 5087 (the remainder is 0, so 1 is a divisor of 5087)
5087 / 2 = 2543.5 (the remainder is 1, so 2 is not a divisor of 5087)
5087 / 3 = 1695.6666666667 (the remainder is 2, so 3 is not a divisor of 5087)
...
5087 / 5086 = 1.0001966181675 (the remainder is 1, so 5086 is not a divisor of 5087)
5087 / 5087 = 1 (the remainder is 0, so 5087 is a divisor of 5087)

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 5087 (i.e. 71.323208004127). 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 $\frac{N}{d} = D$ )

5087 / 1 = 5087 (the remainder is 0, so 1 and 5087 are divisors of 5087)
5087 / 2 = 2543.5 (the remainder is 1, so 2 is not a divisor of 5087)
5087 / 3 = 1695.6666666667 (the remainder is 2, so 3 is not a divisor of 5087)
...
5087 / 70 = 72.671428571429 (the remainder is 47, so 70 is not a divisor of 5087)
5087 / 71 = 71.647887323944 (the remainder is 46, so 71 is not a divisor of 5087)