What are the divisors of 7081?

1, 73, 97, 7081

There is a total of 4 positive divisors.
The sum of these divisors is 7252.
The arithmetic mean is 1813.

4 odd divisors

1, 73, 97, 7081

How to compute the divisors of 7081?

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 7081 by each of the numbers from 1 to 7081 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)

7081 / 1 = 7081 (the remainder is 0, so 1 is a divisor of 7081)
7081 / 2 = 3540.5 (the remainder is 1, so 2 is not a divisor of 7081)
7081 / 3 = 2360.3333333333 (the remainder is 1, so 3 is not a divisor of 7081)
...
7081 / 7080 = 1.0001412429379 (the remainder is 1, so 7080 is not a divisor of 7081)
7081 / 7081 = 1 (the remainder is 0, so 7081 is a divisor of 7081)

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 7081 (i.e. 84.148677945646). 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 $\frac{N}{d} = D$ )

7081 / 1 = 7081 (the remainder is 0, so 1 and 7081 are divisors of 7081)
7081 / 2 = 3540.5 (the remainder is 1, so 2 is not a divisor of 7081)
7081 / 3 = 2360.3333333333 (the remainder is 1, so 3 is not a divisor of 7081)
...
7081 / 83 = 85.313253012048 (the remainder is 26, so 83 is not a divisor of 7081)
7081 / 84 = 84.297619047619 (the remainder is 25, so 84 is not a divisor of 7081)