What are the divisors of 7071?

1, 3, 2357, 7071

There is a total of 4 positive divisors.
The sum of these divisors is 9432.
The arithmetic mean is 2358.

4 odd divisors

1, 3, 2357, 7071

How to compute the divisors of 7071?

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 7071 by each of the numbers from 1 to 7071 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)

7071 / 1 = 7071 (the remainder is 0, so 1 is a divisor of 7071)
7071 / 2 = 3535.5 (the remainder is 1, so 2 is not a divisor of 7071)
7071 / 3 = 2357 (the remainder is 0, so 3 is a divisor of 7071)
...
7071 / 7070 = 1.0001414427157 (the remainder is 1, so 7070 is not a divisor of 7071)
7071 / 7071 = 1 (the remainder is 0, so 7071 is a divisor of 7071)

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 7071 (i.e. 84.08923831264). 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 $\frac{N}{d} = D$ )

7071 / 1 = 7071 (the remainder is 0, so 1 and 7071 are divisors of 7071)
7071 / 2 = 3535.5 (the remainder is 1, so 2 is not a divisor of 7071)
7071 / 3 = 2357 (the remainder is 0, so 3 and 2357 are divisors of 7071)
...
7071 / 83 = 85.192771084337 (the remainder is 16, so 83 is not a divisor of 7071)
7071 / 84 = 84.178571428571 (the remainder is 15, so 84 is not a divisor of 7071)