What are the divisors of 7083?

1, 3, 9, 787, 2361, 7083

There is a total of 6 positive divisors.
The sum of these divisors is 10244.
The arithmetic mean is 1707.3333333333.

6 odd divisors

1, 3, 9, 787, 2361, 7083

How to compute the divisors of 7083?

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 7083 by each of the numbers from 1 to 7083 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)

7083 / 1 = 7083 (the remainder is 0, so 1 is a divisor of 7083)
7083 / 2 = 3541.5 (the remainder is 1, so 2 is not a divisor of 7083)
7083 / 3 = 2361 (the remainder is 0, so 3 is a divisor of 7083)
...
7083 / 7082 = 1.00014120305 (the remainder is 1, so 7082 is not a divisor of 7083)
7083 / 7083 = 1 (the remainder is 0, so 7083 is a divisor of 7083)

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 7083 (i.e. 84.160560834633). 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 $\frac{N}{d} = D$ )

7083 / 1 = 7083 (the remainder is 0, so 1 and 7083 are divisors of 7083)
7083 / 2 = 3541.5 (the remainder is 1, so 2 is not a divisor of 7083)
7083 / 3 = 2361 (the remainder is 0, so 3 and 2361 are divisors of 7083)
...
7083 / 83 = 85.33734939759 (the remainder is 28, so 83 is not a divisor of 7083)
7083 / 84 = 84.321428571429 (the remainder is 27, so 84 is not a divisor of 7083)