What are the divisors of 4083?

1, 3, 1361, 4083

There is a total of 4 positive divisors.
The sum of these divisors is 5448.
The arithmetic mean is 1362.

4 odd divisors

1, 3, 1361, 4083

How to compute the divisors of 4083?

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 4083 by each of the numbers from 1 to 4083 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)

4083 / 1 = 4083 (the remainder is 0, so 1 is a divisor of 4083)
4083 / 2 = 2041.5 (the remainder is 1, so 2 is not a divisor of 4083)
4083 / 3 = 1361 (the remainder is 0, so 3 is a divisor of 4083)
...
4083 / 4082 = 1.000244977952 (the remainder is 1, so 4082 is not a divisor of 4083)
4083 / 4083 = 1 (the remainder is 0, so 4083 is a divisor of 4083)

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 4083 (i.e. 63.898356786384). 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 $\frac{N}{d} = D$ )

4083 / 1 = 4083 (the remainder is 0, so 1 and 4083 are divisors of 4083)
4083 / 2 = 2041.5 (the remainder is 1, so 2 is not a divisor of 4083)
4083 / 3 = 1361 (the remainder is 0, so 3 and 1361 are divisors of 4083)
...
4083 / 62 = 65.854838709677 (the remainder is 53, so 62 is not a divisor of 4083)
4083 / 63 = 64.809523809524 (the remainder is 51, so 63 is not a divisor of 4083)