What are the divisors of 6087?

1, 3, 2029, 6087

There is a total of 4 positive divisors.
The sum of these divisors is 8120.
The arithmetic mean is 2030.

4 odd divisors

1, 3, 2029, 6087

How to compute the divisors of 6087?

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 6087 by each of the numbers from 1 to 6087 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)

6087 / 1 = 6087 (the remainder is 0, so 1 is a divisor of 6087)
6087 / 2 = 3043.5 (the remainder is 1, so 2 is not a divisor of 6087)
6087 / 3 = 2029 (the remainder is 0, so 3 is a divisor of 6087)
...
6087 / 6086 = 1.0001643115347 (the remainder is 1, so 6086 is not a divisor of 6087)
6087 / 6087 = 1 (the remainder is 0, so 6087 is a divisor of 6087)

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 6087 (i.e. 78.019228399158). 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 $\frac{N}{d} = D$ )

6087 / 1 = 6087 (the remainder is 0, so 1 and 6087 are divisors of 6087)
6087 / 2 = 3043.5 (the remainder is 1, so 2 is not a divisor of 6087)
6087 / 3 = 2029 (the remainder is 0, so 3 and 2029 are divisors of 6087)
...
6087 / 77 = 79.051948051948 (the remainder is 4, so 77 is not a divisor of 6087)
6087 / 78 = 78.038461538462 (the remainder is 3, so 78 is not a divisor of 6087)