What are the divisors of 4081?

1, 7, 11, 53, 77, 371, 583, 4081

There is a total of 8 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 648.

8 odd divisors

1, 7, 11, 53, 77, 371, 583, 4081

How to compute the divisors of 4081?

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 4081 by each of the numbers from 1 to 4081 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)

4081 / 1 = 4081 (the remainder is 0, so 1 is a divisor of 4081)
4081 / 2 = 2040.5 (the remainder is 1, so 2 is not a divisor of 4081)
4081 / 3 = 1360.3333333333 (the remainder is 1, so 3 is not a divisor of 4081)
...
4081 / 4080 = 1.0002450980392 (the remainder is 1, so 4080 is not a divisor of 4081)
4081 / 4081 = 1 (the remainder is 0, so 4081 is a divisor of 4081)

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 4081 (i.e. 63.882705014738). 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 $\frac{N}{d} = D$ )

4081 / 1 = 4081 (the remainder is 0, so 1 and 4081 are divisors of 4081)
4081 / 2 = 2040.5 (the remainder is 1, so 2 is not a divisor of 4081)
4081 / 3 = 1360.3333333333 (the remainder is 1, so 3 is not a divisor of 4081)
...
4081 / 62 = 65.822580645161 (the remainder is 51, so 62 is not a divisor of 4081)
4081 / 63 = 64.777777777778 (the remainder is 49, so 63 is not a divisor of 4081)