What are the divisors of 7092?

1, 2, 3, 4, 6, 9, 12, 18, 36, 197, 394, 591, 788, 1182, 1773, 2364, 3546, 7092

There is a total of 18 positive divisors.
The sum of these divisors is 18018.
The arithmetic mean is 1001.

12 even divisors

2, 4, 6, 12, 18, 36, 394, 788, 1182, 2364, 3546, 7092

6 odd divisors

1, 3, 9, 197, 591, 1773

How to compute the divisors of 7092?

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 7092 by each of the numbers from 1 to 7092 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)

7092 / 1 = 7092 (the remainder is 0, so 1 is a divisor of 7092)
7092 / 2 = 3546 (the remainder is 0, so 2 is a divisor of 7092)
7092 / 3 = 2364 (the remainder is 0, so 3 is a divisor of 7092)
...
7092 / 7091 = 1.000141023833 (the remainder is 1, so 7091 is not a divisor of 7092)
7092 / 7092 = 1 (the remainder is 0, so 7092 is a divisor of 7092)

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 7092 (i.e. 84.214013085709). 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 $\frac{N}{d} = D$ )

7092 / 1 = 7092 (the remainder is 0, so 1 and 7092 are divisors of 7092)
7092 / 2 = 3546 (the remainder is 0, so 2 and 3546 are divisors of 7092)
7092 / 3 = 2364 (the remainder is 0, so 3 and 2364 are divisors of 7092)
...
7092 / 83 = 85.44578313253 (the remainder is 37, so 83 is not a divisor of 7092)
7092 / 84 = 84.428571428571 (the remainder is 36, so 84 is not a divisor of 7092)