What are the divisors of 8075?

1, 5, 17, 19, 25, 85, 95, 323, 425, 475, 1615, 8075

There is a total of 12 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 930.

12 odd divisors

1, 5, 17, 19, 25, 85, 95, 323, 425, 475, 1615, 8075

How to compute the divisors of 8075?

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 8075 by each of the numbers from 1 to 8075 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)

8075 / 1 = 8075 (the remainder is 0, so 1 is a divisor of 8075)
8075 / 2 = 4037.5 (the remainder is 1, so 2 is not a divisor of 8075)
8075 / 3 = 2691.6666666667 (the remainder is 2, so 3 is not a divisor of 8075)
...
8075 / 8074 = 1.0001238543473 (the remainder is 1, so 8074 is not a divisor of 8075)
8075 / 8075 = 1 (the remainder is 0, so 8075 is a divisor of 8075)

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 8075 (i.e. 89.861003778057). 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 $\frac{N}{d} = D$ )

8075 / 1 = 8075 (the remainder is 0, so 1 and 8075 are divisors of 8075)
8075 / 2 = 4037.5 (the remainder is 1, so 2 is not a divisor of 8075)
8075 / 3 = 2691.6666666667 (the remainder is 2, so 3 is not a divisor of 8075)
...
8075 / 88 = 91.761363636364 (the remainder is 67, so 88 is not a divisor of 8075)
8075 / 89 = 90.730337078652 (the remainder is 65, so 89 is not a divisor of 8075)