What are the divisors of 7060?

1, 2, 4, 5, 10, 20, 353, 706, 1412, 1765, 3530, 7060

There is a total of 12 positive divisors.
The sum of these divisors is 14868.
The arithmetic mean is 1239.

8 even divisors

2, 4, 10, 20, 706, 1412, 3530, 7060

4 odd divisors

1, 5, 353, 1765

How to compute the divisors of 7060?

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 7060 by each of the numbers from 1 to 7060 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)

7060 / 1 = 7060 (the remainder is 0, so 1 is a divisor of 7060)
7060 / 2 = 3530 (the remainder is 0, so 2 is a divisor of 7060)
7060 / 3 = 2353.3333333333 (the remainder is 1, so 3 is not a divisor of 7060)
...
7060 / 7059 = 1.0001416631251 (the remainder is 1, so 7059 is not a divisor of 7060)
7060 / 7060 = 1 (the remainder is 0, so 7060 is a divisor of 7060)

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 7060 (i.e. 84.0238061504). 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 $\frac{N}{d} = D$ )

7060 / 1 = 7060 (the remainder is 0, so 1 and 7060 are divisors of 7060)
7060 / 2 = 3530 (the remainder is 0, so 2 and 3530 are divisors of 7060)
7060 / 3 = 2353.3333333333 (the remainder is 1, so 3 is not a divisor of 7060)
...
7060 / 83 = 85.060240963855 (the remainder is 5, so 83 is not a divisor of 7060)
7060 / 84 = 84.047619047619 (the remainder is 4, so 84 is not a divisor of 7060)