What are the divisors of 6089?

1, 6089

There is a total of 2 positive divisors.
The sum of these divisors is 6090.
The arithmetic mean is 3045.

2 odd divisors

1, 6089

How to compute the divisors of 6089?

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 6089 by each of the numbers from 1 to 6089 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)

6089 / 1 = 6089 (the remainder is 0, so 1 is a divisor of 6089)
6089 / 2 = 3044.5 (the remainder is 1, so 2 is not a divisor of 6089)
6089 / 3 = 2029.6666666667 (the remainder is 2, so 3 is not a divisor of 6089)
...
6089 / 6088 = 1.0001642575558 (the remainder is 1, so 6088 is not a divisor of 6089)
6089 / 6089 = 1 (the remainder is 0, so 6089 is a divisor of 6089)

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 6089 (i.e. 78.032044699598). 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 $\frac{N}{d} = D$ )

6089 / 1 = 6089 (the remainder is 0, so 1 and 6089 are divisors of 6089)
6089 / 2 = 3044.5 (the remainder is 1, so 2 is not a divisor of 6089)
6089 / 3 = 2029.6666666667 (the remainder is 2, so 3 is not a divisor of 6089)
...
6089 / 77 = 79.077922077922 (the remainder is 6, so 77 is not a divisor of 6089)
6089 / 78 = 78.064102564103 (the remainder is 5, so 78 is not a divisor of 6089)