What are the divisors of 7095?

1, 3, 5, 11, 15, 33, 43, 55, 129, 165, 215, 473, 645, 1419, 2365, 7095

There is a total of 16 positive divisors.
The sum of these divisors is 12672.
The arithmetic mean is 792.

16 odd divisors

1, 3, 5, 11, 15, 33, 43, 55, 129, 165, 215, 473, 645, 1419, 2365, 7095

How to compute the divisors of 7095?

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 7095 by each of the numbers from 1 to 7095 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)

7095 / 1 = 7095 (the remainder is 0, so 1 is a divisor of 7095)
7095 / 2 = 3547.5 (the remainder is 1, so 2 is not a divisor of 7095)
7095 / 3 = 2365 (the remainder is 0, so 3 is a divisor of 7095)
...
7095 / 7094 = 1.0001409641951 (the remainder is 1, so 7094 is not a divisor of 7095)
7095 / 7095 = 1 (the remainder is 0, so 7095 is a divisor of 7095)

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 7095 (i.e. 84.231822964958). 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 $\frac{N}{d} = D$ )

7095 / 1 = 7095 (the remainder is 0, so 1 and 7095 are divisors of 7095)
7095 / 2 = 3547.5 (the remainder is 1, so 2 is not a divisor of 7095)
7095 / 3 = 2365 (the remainder is 0, so 3 and 2365 are divisors of 7095)
...
7095 / 83 = 85.481927710843 (the remainder is 40, so 83 is not a divisor of 7095)
7095 / 84 = 84.464285714286 (the remainder is 39, so 84 is not a divisor of 7095)