What are the divisors of 7082?

1, 2, 3541, 7082

There is a total of 4 positive divisors.
The sum of these divisors is 10626.
The arithmetic mean is 2656.5.

2 even divisors

2, 7082

2 odd divisors

1, 3541

How to compute the divisors of 7082?

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 7082 by each of the numbers from 1 to 7082 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)

7082 / 1 = 7082 (the remainder is 0, so 1 is a divisor of 7082)
7082 / 2 = 3541 (the remainder is 0, so 2 is a divisor of 7082)
7082 / 3 = 2360.6666666667 (the remainder is 2, so 3 is not a divisor of 7082)
...
7082 / 7081 = 1.0001412229911 (the remainder is 1, so 7081 is not a divisor of 7082)
7082 / 7082 = 1 (the remainder is 0, so 7082 is a divisor of 7082)

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 7082 (i.e. 84.154619599877). 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 $\frac{N}{d} = D$ )

7082 / 1 = 7082 (the remainder is 0, so 1 and 7082 are divisors of 7082)
7082 / 2 = 3541 (the remainder is 0, so 2 and 3541 are divisors of 7082)
7082 / 3 = 2360.6666666667 (the remainder is 2, so 3 is not a divisor of 7082)
...
7082 / 83 = 85.325301204819 (the remainder is 27, so 83 is not a divisor of 7082)
7082 / 84 = 84.309523809524 (the remainder is 26, so 84 is not a divisor of 7082)