What are the divisors of 7093?

1, 41, 173, 7093

There is a total of 4 positive divisors.
The sum of these divisors is 7308.
The arithmetic mean is 1827.

4 odd divisors

1, 41, 173, 7093

How to compute the divisors of 7093?

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 7093 by each of the numbers from 1 to 7093 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)

7093 / 1 = 7093 (the remainder is 0, so 1 is a divisor of 7093)
7093 / 2 = 3546.5 (the remainder is 1, so 2 is not a divisor of 7093)
7093 / 3 = 2364.3333333333 (the remainder is 1, so 3 is not a divisor of 7093)
...
7093 / 7092 = 1.0001410039481 (the remainder is 1, so 7092 is not a divisor of 7093)
7093 / 7093 = 1 (the remainder is 0, so 7093 is a divisor of 7093)

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 7093 (i.e. 84.219950130596). 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 $\frac{N}{d} = D$ )

7093 / 1 = 7093 (the remainder is 0, so 1 and 7093 are divisors of 7093)
7093 / 2 = 3546.5 (the remainder is 1, so 2 is not a divisor of 7093)
7093 / 3 = 2364.3333333333 (the remainder is 1, so 3 is not a divisor of 7093)
...
7093 / 83 = 85.457831325301 (the remainder is 38, so 83 is not a divisor of 7093)
7093 / 84 = 84.440476190476 (the remainder is 37, so 84 is not a divisor of 7093)