What are the divisors of 3081?

1, 3, 13, 39, 79, 237, 1027, 3081

There is a total of 8 positive divisors.
The sum of these divisors is 4480.
The arithmetic mean is 560.

8 odd divisors

1, 3, 13, 39, 79, 237, 1027, 3081

How to compute the divisors of 3081?

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 3081 by each of the numbers from 1 to 3081 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)

3081 / 1 = 3081 (the remainder is 0, so 1 is a divisor of 3081)
3081 / 2 = 1540.5 (the remainder is 1, so 2 is not a divisor of 3081)
3081 / 3 = 1027 (the remainder is 0, so 3 is a divisor of 3081)
...
3081 / 3080 = 1.0003246753247 (the remainder is 1, so 3080 is not a divisor of 3081)
3081 / 3081 = 1 (the remainder is 0, so 3081 is a divisor of 3081)

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 3081 (i.e. 55.506756345512). 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 $\frac{N}{d} = D$ )

3081 / 1 = 3081 (the remainder is 0, so 1 and 3081 are divisors of 3081)
3081 / 2 = 1540.5 (the remainder is 1, so 2 is not a divisor of 3081)
3081 / 3 = 1027 (the remainder is 0, so 3 and 1027 are divisors of 3081)
...
3081 / 54 = 57.055555555556 (the remainder is 3, so 54 is not a divisor of 3081)
3081 / 55 = 56.018181818182 (the remainder is 1, so 55 is not a divisor of 3081)