What are the divisors of 7075?

1, 5, 25, 283, 1415, 7075

There is a total of 6 positive divisors.
The sum of these divisors is 8804.
The arithmetic mean is 1467.3333333333.

6 odd divisors

1, 5, 25, 283, 1415, 7075

How to compute the divisors of 7075?

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 7075 by each of the numbers from 1 to 7075 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)

7075 / 1 = 7075 (the remainder is 0, so 1 is a divisor of 7075)
7075 / 2 = 3537.5 (the remainder is 1, so 2 is not a divisor of 7075)
7075 / 3 = 2358.3333333333 (the remainder is 1, so 3 is not a divisor of 7075)
...
7075 / 7074 = 1.0001413627368 (the remainder is 1, so 7074 is not a divisor of 7075)
7075 / 7075 = 1 (the remainder is 0, so 7075 is a divisor of 7075)

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 7075 (i.e. 84.113019206304). 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 $\frac{N}{d} = D$ )

7075 / 1 = 7075 (the remainder is 0, so 1 and 7075 are divisors of 7075)
7075 / 2 = 3537.5 (the remainder is 1, so 2 is not a divisor of 7075)
7075 / 3 = 2358.3333333333 (the remainder is 1, so 3 is not a divisor of 7075)
...
7075 / 83 = 85.240963855422 (the remainder is 20, so 83 is not a divisor of 7075)
7075 / 84 = 84.22619047619 (the remainder is 19, so 84 is not a divisor of 7075)