What are the divisors of 7055?

1, 5, 17, 83, 85, 415, 1411, 7055

There is a total of 8 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 1134.

8 odd divisors

1, 5, 17, 83, 85, 415, 1411, 7055

How to compute the divisors of 7055?

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 7055 by each of the numbers from 1 to 7055 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)

7055 / 1 = 7055 (the remainder is 0, so 1 is a divisor of 7055)
7055 / 2 = 3527.5 (the remainder is 1, so 2 is not a divisor of 7055)
7055 / 3 = 2351.6666666667 (the remainder is 2, so 3 is not a divisor of 7055)
...
7055 / 7054 = 1.0001417635384 (the remainder is 1, so 7054 is not a divisor of 7055)
7055 / 7055 = 1 (the remainder is 0, so 7055 is a divisor of 7055)

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 7055 (i.e. 83.994047408135). 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 $\frac{N}{d} = D$ )

7055 / 1 = 7055 (the remainder is 0, so 1 and 7055 are divisors of 7055)
7055 / 2 = 3527.5 (the remainder is 1, so 2 is not a divisor of 7055)
7055 / 3 = 2351.6666666667 (the remainder is 2, so 3 is not a divisor of 7055)
...
7055 / 82 = 86.036585365854 (the remainder is 3, so 82 is not a divisor of 7055)
7055 / 83 = 85 (the remainder is 0, so 83 and 85 are divisors of 7055)