What are the divisors of 8265?

1, 3, 5, 15, 19, 29, 57, 87, 95, 145, 285, 435, 551, 1653, 2755, 8265

There is a total of 16 positive divisors.
The sum of these divisors is 14400.
The arithmetic mean is 900.

16 odd divisors

1, 3, 5, 15, 19, 29, 57, 87, 95, 145, 285, 435, 551, 1653, 2755, 8265

How to compute the divisors of 8265?

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 8265 by each of the numbers from 1 to 8265 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)

8265 / 1 = 8265 (the remainder is 0, so 1 is a divisor of 8265)
8265 / 2 = 4132.5 (the remainder is 1, so 2 is not a divisor of 8265)
8265 / 3 = 2755 (the remainder is 0, so 3 is a divisor of 8265)
...
8265 / 8264 = 1.0001210067764 (the remainder is 1, so 8264 is not a divisor of 8265)
8265 / 8265 = 1 (the remainder is 0, so 8265 is a divisor of 8265)

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 8265 (i.e. 90.912045406536). 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 $\frac{N}{d} = D$ )

8265 / 1 = 8265 (the remainder is 0, so 1 and 8265 are divisors of 8265)
8265 / 2 = 4132.5 (the remainder is 1, so 2 is not a divisor of 8265)
8265 / 3 = 2755 (the remainder is 0, so 3 and 2755 are divisors of 8265)
...
8265 / 89 = 92.865168539326 (the remainder is 77, so 89 is not a divisor of 8265)
8265 / 90 = 91.833333333333 (the remainder is 75, so 90 is not a divisor of 8265)