What are the divisors of 7015?

1, 5, 23, 61, 115, 305, 1403, 7015

There is a total of 8 positive divisors.
The sum of these divisors is 8928.
The arithmetic mean is 1116.

8 odd divisors

1, 5, 23, 61, 115, 305, 1403, 7015

How to compute the divisors of 7015?

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 7015 by each of the numbers from 1 to 7015 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)

7015 / 1 = 7015 (the remainder is 0, so 1 is a divisor of 7015)
7015 / 2 = 3507.5 (the remainder is 1, so 2 is not a divisor of 7015)
7015 / 3 = 2338.3333333333 (the remainder is 1, so 3 is not a divisor of 7015)
...
7015 / 7014 = 1.0001425719989 (the remainder is 1, so 7014 is not a divisor of 7015)
7015 / 7015 = 1 (the remainder is 0, so 7015 is a divisor of 7015)

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 7015 (i.e. 83.755596827914). 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 $\frac{N}{d} = D$ )

7015 / 1 = 7015 (the remainder is 0, so 1 and 7015 are divisors of 7015)
7015 / 2 = 3507.5 (the remainder is 1, so 2 is not a divisor of 7015)
7015 / 3 = 2338.3333333333 (the remainder is 1, so 3 is not a divisor of 7015)
...
7015 / 82 = 85.548780487805 (the remainder is 45, so 82 is not a divisor of 7015)
7015 / 83 = 84.518072289157 (the remainder is 43, so 83 is not a divisor of 7015)