What are the divisors of 7061?

1, 23, 307, 7061

There is a total of 4 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 1848.

4 odd divisors

1, 23, 307, 7061

How to compute the divisors of 7061?

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 7061 by each of the numbers from 1 to 7061 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)

7061 / 1 = 7061 (the remainder is 0, so 1 is a divisor of 7061)
7061 / 2 = 3530.5 (the remainder is 1, so 2 is not a divisor of 7061)
7061 / 3 = 2353.6666666667 (the remainder is 2, so 3 is not a divisor of 7061)
...
7061 / 7060 = 1.0001416430595 (the remainder is 1, so 7060 is not a divisor of 7061)
7061 / 7061 = 1 (the remainder is 0, so 7061 is a divisor of 7061)

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 7061 (i.e. 84.029756634183). 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 $\frac{N}{d} = D$ )

7061 / 1 = 7061 (the remainder is 0, so 1 and 7061 are divisors of 7061)
7061 / 2 = 3530.5 (the remainder is 1, so 2 is not a divisor of 7061)
7061 / 3 = 2353.6666666667 (the remainder is 2, so 3 is not a divisor of 7061)
...
7061 / 83 = 85.072289156627 (the remainder is 6, so 83 is not a divisor of 7061)
7061 / 84 = 84.059523809524 (the remainder is 5, so 84 is not a divisor of 7061)