What are the divisors of 8275?

1, 5, 25, 331, 1655, 8275

There is a total of 6 positive divisors.
The sum of these divisors is 10292.
The arithmetic mean is 1715.3333333333.

6 odd divisors

1, 5, 25, 331, 1655, 8275

How to compute the divisors of 8275?

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 8275 by each of the numbers from 1 to 8275 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)

8275 / 1 = 8275 (the remainder is 0, so 1 is a divisor of 8275)
8275 / 2 = 4137.5 (the remainder is 1, so 2 is not a divisor of 8275)
8275 / 3 = 2758.3333333333 (the remainder is 1, so 3 is not a divisor of 8275)
...
8275 / 8274 = 1.000120860527 (the remainder is 1, so 8274 is not a divisor of 8275)
8275 / 8275 = 1 (the remainder is 0, so 8275 is a divisor of 8275)

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 8275 (i.e. 90.967026993301). 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 $\frac{N}{d} = D$ )

8275 / 1 = 8275 (the remainder is 0, so 1 and 8275 are divisors of 8275)
8275 / 2 = 4137.5 (the remainder is 1, so 2 is not a divisor of 8275)
8275 / 3 = 2758.3333333333 (the remainder is 1, so 3 is not a divisor of 8275)
...
8275 / 89 = 92.977528089888 (the remainder is 87, so 89 is not a divisor of 8275)
8275 / 90 = 91.944444444444 (the remainder is 85, so 90 is not a divisor of 8275)