What are the divisors of 5587?

1, 37, 151, 5587

There is a total of 4 positive divisors.
The sum of these divisors is 5776.
The arithmetic mean is 1444.

4 odd divisors

1, 37, 151, 5587

How to compute the divisors of 5587?

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 5587 by each of the numbers from 1 to 5587 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)

5587 / 1 = 5587 (the remainder is 0, so 1 is a divisor of 5587)
5587 / 2 = 2793.5 (the remainder is 1, so 2 is not a divisor of 5587)
5587 / 3 = 1862.3333333333 (the remainder is 1, so 3 is not a divisor of 5587)
...
5587 / 5586 = 1.000179018976 (the remainder is 1, so 5586 is not a divisor of 5587)
5587 / 5587 = 1 (the remainder is 0, so 5587 is a divisor of 5587)

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 5587 (i.e. 74.746237363495). 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 $\frac{N}{d} = D$ )

5587 / 1 = 5587 (the remainder is 0, so 1 and 5587 are divisors of 5587)
5587 / 2 = 2793.5 (the remainder is 1, so 2 is not a divisor of 5587)
5587 / 3 = 1862.3333333333 (the remainder is 1, so 3 is not a divisor of 5587)
...
5587 / 73 = 76.534246575342 (the remainder is 39, so 73 is not a divisor of 5587)
5587 / 74 = 75.5 (the remainder is 37, so 74 is not a divisor of 5587)