What are the divisors of 4041?

1, 3, 9, 449, 1347, 4041

There is a total of 6 positive divisors.
The sum of these divisors is 5850.
The arithmetic mean is 975.

6 odd divisors

1, 3, 9, 449, 1347, 4041

How to compute the divisors of 4041?

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 4041 by each of the numbers from 1 to 4041 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)

4041 / 1 = 4041 (the remainder is 0, so 1 is a divisor of 4041)
4041 / 2 = 2020.5 (the remainder is 1, so 2 is not a divisor of 4041)
4041 / 3 = 1347 (the remainder is 0, so 3 is a divisor of 4041)
...
4041 / 4040 = 1.0002475247525 (the remainder is 1, so 4040 is not a divisor of 4041)
4041 / 4041 = 1 (the remainder is 0, so 4041 is a divisor of 4041)

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 4041 (i.e. 63.568860301251). 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 $\frac{N}{d} = D$ )

4041 / 1 = 4041 (the remainder is 0, so 1 and 4041 are divisors of 4041)
4041 / 2 = 2020.5 (the remainder is 1, so 2 is not a divisor of 4041)
4041 / 3 = 1347 (the remainder is 0, so 3 and 1347 are divisors of 4041)
...
4041 / 62 = 65.177419354839 (the remainder is 11, so 62 is not a divisor of 4041)
4041 / 63 = 64.142857142857 (the remainder is 9, so 63 is not a divisor of 4041)