What are the divisors of 7073?

1, 11, 643, 7073

There is a total of 4 positive divisors.
The sum of these divisors is 7728.
The arithmetic mean is 1932.

4 odd divisors

1, 11, 643, 7073

How to compute the divisors of 7073?

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 7073 by each of the numbers from 1 to 7073 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)

7073 / 1 = 7073 (the remainder is 0, so 1 is a divisor of 7073)
7073 / 2 = 3536.5 (the remainder is 1, so 2 is not a divisor of 7073)
7073 / 3 = 2357.6666666667 (the remainder is 2, so 3 is not a divisor of 7073)
...
7073 / 7072 = 1.0001414027149 (the remainder is 1, so 7072 is not a divisor of 7073)
7073 / 7073 = 1 (the remainder is 0, so 7073 is a divisor of 7073)

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 7073 (i.e. 84.101129600024). 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 $\frac{N}{d} = D$ )

7073 / 1 = 7073 (the remainder is 0, so 1 and 7073 are divisors of 7073)
7073 / 2 = 3536.5 (the remainder is 1, so 2 is not a divisor of 7073)
7073 / 3 = 2357.6666666667 (the remainder is 2, so 3 is not a divisor of 7073)
...
7073 / 83 = 85.21686746988 (the remainder is 18, so 83 is not a divisor of 7073)
7073 / 84 = 84.202380952381 (the remainder is 17, so 84 is not a divisor of 7073)