What are the divisors of 7096?

1, 2, 4, 8, 887, 1774, 3548, 7096

There is a total of 8 positive divisors.
The sum of these divisors is 13320.
The arithmetic mean is 1665.

6 even divisors

2, 4, 8, 1774, 3548, 7096

2 odd divisors

1, 887

How to compute the divisors of 7096?

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 7096 by each of the numbers from 1 to 7096 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)

7096 / 1 = 7096 (the remainder is 0, so 1 is a divisor of 7096)
7096 / 2 = 3548 (the remainder is 0, so 2 is a divisor of 7096)
7096 / 3 = 2365.3333333333 (the remainder is 1, so 3 is not a divisor of 7096)
...
7096 / 7095 = 1.000140944327 (the remainder is 1, so 7095 is not a divisor of 7096)
7096 / 7096 = 1 (the remainder is 0, so 7096 is a divisor of 7096)

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 7096 (i.e. 84.237758754611). 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 $\frac{N}{d} = D$ )

7096 / 1 = 7096 (the remainder is 0, so 1 and 7096 are divisors of 7096)
7096 / 2 = 3548 (the remainder is 0, so 2 and 3548 are divisors of 7096)
7096 / 3 = 2365.3333333333 (the remainder is 1, so 3 is not a divisor of 7096)
...
7096 / 83 = 85.493975903614 (the remainder is 41, so 83 is not a divisor of 7096)
7096 / 84 = 84.47619047619 (the remainder is 40, so 84 is not a divisor of 7096)