What are the divisors of 7084?

1, 2, 4, 7, 11, 14, 22, 23, 28, 44, 46, 77, 92, 154, 161, 253, 308, 322, 506, 644, 1012, 1771, 3542, 7084

There is a total of 24 positive divisors.
The sum of these divisors is 16128.
The arithmetic mean is 672.

16 even divisors

2, 4, 14, 22, 28, 44, 46, 92, 154, 308, 322, 506, 644, 1012, 3542, 7084

8 odd divisors

1, 7, 11, 23, 77, 161, 253, 1771

How to compute the divisors of 7084?

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 7084 by each of the numbers from 1 to 7084 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)

7084 / 1 = 7084 (the remainder is 0, so 1 is a divisor of 7084)
7084 / 2 = 3542 (the remainder is 0, so 2 is a divisor of 7084)
7084 / 3 = 2361.3333333333 (the remainder is 1, so 3 is not a divisor of 7084)
...
7084 / 7083 = 1.0001411831145 (the remainder is 1, so 7083 is not a divisor of 7084)
7084 / 7084 = 1 (the remainder is 0, so 7084 is a divisor of 7084)

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 7084 (i.e. 84.166501650003). 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 $\frac{N}{d} = D$ )

7084 / 1 = 7084 (the remainder is 0, so 1 and 7084 are divisors of 7084)
7084 / 2 = 3542 (the remainder is 0, so 2 and 3542 are divisors of 7084)
7084 / 3 = 2361.3333333333 (the remainder is 1, so 3 is not a divisor of 7084)
...
7084 / 83 = 85.349397590361 (the remainder is 29, so 83 is not a divisor of 7084)
7084 / 84 = 84.333333333333 (the remainder is 28, so 84 is not a divisor of 7084)