What are the divisors of 7076?

1, 2, 4, 29, 58, 61, 116, 122, 244, 1769, 3538, 7076

There is a total of 12 positive divisors.
The sum of these divisors is 13020.
The arithmetic mean is 1085.

8 even divisors

2, 4, 58, 116, 122, 244, 3538, 7076

4 odd divisors

1, 29, 61, 1769

How to compute the divisors of 7076?

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 7076 by each of the numbers from 1 to 7076 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)

7076 / 1 = 7076 (the remainder is 0, so 1 is a divisor of 7076)
7076 / 2 = 3538 (the remainder is 0, so 2 is a divisor of 7076)
7076 / 3 = 2358.6666666667 (the remainder is 2, so 3 is not a divisor of 7076)
...
7076 / 7075 = 1.0001413427562 (the remainder is 1, so 7075 is not a divisor of 7076)
7076 / 7076 = 1 (the remainder is 0, so 7076 is a divisor of 7076)

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 7076 (i.e. 84.118963379252). 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 $\frac{N}{d} = D$ )

7076 / 1 = 7076 (the remainder is 0, so 1 and 7076 are divisors of 7076)
7076 / 2 = 3538 (the remainder is 0, so 2 and 3538 are divisors of 7076)
7076 / 3 = 2358.6666666667 (the remainder is 2, so 3 is not a divisor of 7076)
...
7076 / 83 = 85.253012048193 (the remainder is 21, so 83 is not a divisor of 7076)
7076 / 84 = 84.238095238095 (the remainder is 20, so 84 is not a divisor of 7076)