What are the divisors of 6043?

1, 6043

There is a total of 2 positive divisors.
The sum of these divisors is 6044.
The arithmetic mean is 3022.

2 odd divisors

1, 6043

How to compute the divisors of 6043?

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 6043 by each of the numbers from 1 to 6043 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)

6043 / 1 = 6043 (the remainder is 0, so 1 is a divisor of 6043)
6043 / 2 = 3021.5 (the remainder is 1, so 2 is not a divisor of 6043)
6043 / 3 = 2014.3333333333 (the remainder is 1, so 3 is not a divisor of 6043)
...
6043 / 6042 = 1.0001655081099 (the remainder is 1, so 6042 is not a divisor of 6043)
6043 / 6043 = 1 (the remainder is 0, so 6043 is a divisor of 6043)

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 6043 (i.e. 77.736735202863). 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 $\frac{N}{d} = D$ )

6043 / 1 = 6043 (the remainder is 0, so 1 and 6043 are divisors of 6043)
6043 / 2 = 3021.5 (the remainder is 1, so 2 is not a divisor of 6043)
6043 / 3 = 2014.3333333333 (the remainder is 1, so 3 is not a divisor of 6043)
...
6043 / 76 = 79.513157894737 (the remainder is 39, so 76 is not a divisor of 6043)
6043 / 77 = 78.480519480519 (the remainder is 37, so 77 is not a divisor of 6043)