What are the divisors of 8015?

1, 5, 7, 35, 229, 1145, 1603, 8015

There is a total of 8 positive divisors.
The sum of these divisors is 11040.
The arithmetic mean is 1380.

8 odd divisors

1, 5, 7, 35, 229, 1145, 1603, 8015

How to compute the divisors of 8015?

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 8015 by each of the numbers from 1 to 8015 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)

8015 / 1 = 8015 (the remainder is 0, so 1 is a divisor of 8015)
8015 / 2 = 4007.5 (the remainder is 1, so 2 is not a divisor of 8015)
8015 / 3 = 2671.6666666667 (the remainder is 2, so 3 is not a divisor of 8015)
...
8015 / 8014 = 1.0001247816321 (the remainder is 1, so 8014 is not a divisor of 8015)
8015 / 8015 = 1 (the remainder is 0, so 8015 is a divisor of 8015)

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 8015 (i.e. 89.526532380072). 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 $\frac{N}{d} = D$ )

8015 / 1 = 8015 (the remainder is 0, so 1 and 8015 are divisors of 8015)
8015 / 2 = 4007.5 (the remainder is 1, so 2 is not a divisor of 8015)
8015 / 3 = 2671.6666666667 (the remainder is 2, so 3 is not a divisor of 8015)
...
8015 / 88 = 91.079545454545 (the remainder is 7, so 88 is not a divisor of 8015)
8015 / 89 = 90.056179775281 (the remainder is 5, so 89 is not a divisor of 8015)