What are the divisors of 5987?

1, 5987

There is a total of 2 positive divisors.
The sum of these divisors is 5988.
The arithmetic mean is 2994.

2 odd divisors

1, 5987

How to compute the divisors of 5987?

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 5987 by each of the numbers from 1 to 5987 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)

5987 / 1 = 5987 (the remainder is 0, so 1 is a divisor of 5987)
5987 / 2 = 2993.5 (the remainder is 1, so 2 is not a divisor of 5987)
5987 / 3 = 1995.6666666667 (the remainder is 2, so 3 is not a divisor of 5987)
...
5987 / 5986 = 1.0001670564651 (the remainder is 1, so 5986 is not a divisor of 5987)
5987 / 5987 = 1 (the remainder is 0, so 5987 is a divisor of 5987)

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 5987 (i.e. 77.375706781909). 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 $\frac{N}{d} = D$ )

5987 / 1 = 5987 (the remainder is 0, so 1 and 5987 are divisors of 5987)
5987 / 2 = 2993.5 (the remainder is 1, so 2 is not a divisor of 5987)
5987 / 3 = 1995.6666666667 (the remainder is 2, so 3 is not a divisor of 5987)
...
5987 / 76 = 78.776315789474 (the remainder is 59, so 76 is not a divisor of 5987)
5987 / 77 = 77.753246753247 (the remainder is 58, so 77 is not a divisor of 5987)