What are the divisors of 6047?

1, 6047

There is a total of 2 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 3024.

2 odd divisors

1, 6047

How to compute the divisors of 6047?

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 6047 by each of the numbers from 1 to 6047 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)

6047 / 1 = 6047 (the remainder is 0, so 1 is a divisor of 6047)
6047 / 2 = 3023.5 (the remainder is 1, so 2 is not a divisor of 6047)
6047 / 3 = 2015.6666666667 (the remainder is 2, so 3 is not a divisor of 6047)
...
6047 / 6046 = 1.0001653986107 (the remainder is 1, so 6046 is not a divisor of 6047)
6047 / 6047 = 1 (the remainder is 0, so 6047 is a divisor of 6047)

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 6047 (i.e. 77.762458808862). 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 $\frac{N}{d} = D$ )

6047 / 1 = 6047 (the remainder is 0, so 1 and 6047 are divisors of 6047)
6047 / 2 = 3023.5 (the remainder is 1, so 2 is not a divisor of 6047)
6047 / 3 = 2015.6666666667 (the remainder is 2, so 3 is not a divisor of 6047)
...
6047 / 76 = 79.565789473684 (the remainder is 43, so 76 is not a divisor of 6047)
6047 / 77 = 78.532467532468 (the remainder is 41, so 77 is not a divisor of 6047)