What are the divisors of 6041?

1, 7, 863, 6041

There is a total of 4 positive divisors.
The sum of these divisors is 6912.
The arithmetic mean is 1728.

4 odd divisors

1, 7, 863, 6041

How to compute the divisors of 6041?

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 6041 by each of the numbers from 1 to 6041 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)

6041 / 1 = 6041 (the remainder is 0, so 1 is a divisor of 6041)
6041 / 2 = 3020.5 (the remainder is 1, so 2 is not a divisor of 6041)
6041 / 3 = 2013.6666666667 (the remainder is 2, so 3 is not a divisor of 6041)
...
6041 / 6040 = 1.0001655629139 (the remainder is 1, so 6040 is not a divisor of 6041)
6041 / 6041 = 1 (the remainder is 0, so 6041 is a divisor of 6041)

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 6041 (i.e. 77.723870207292). 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 $\frac{N}{d} = D$ )

6041 / 1 = 6041 (the remainder is 0, so 1 and 6041 are divisors of 6041)
6041 / 2 = 3020.5 (the remainder is 1, so 2 is not a divisor of 6041)
6041 / 3 = 2013.6666666667 (the remainder is 2, so 3 is not a divisor of 6041)
...
6041 / 76 = 79.486842105263 (the remainder is 37, so 76 is not a divisor of 6041)
6041 / 77 = 78.454545454545 (the remainder is 35, so 77 is not a divisor of 6041)