What are the divisors of 8250?

1, 2, 3, 5, 6, 10, 11, 15, 22, 25, 30, 33, 50, 55, 66, 75, 110, 125, 150, 165, 250, 275, 330, 375, 550, 750, 825, 1375, 1650, 2750, 4125, 8250

There is a total of 32 positive divisors.
The sum of these divisors is 22464.
The arithmetic mean is 702.

16 even divisors

2, 6, 10, 22, 30, 50, 66, 110, 150, 250, 330, 550, 750, 1650, 2750, 8250

16 odd divisors

1, 3, 5, 11, 15, 25, 33, 55, 75, 125, 165, 275, 375, 825, 1375, 4125

How to compute the divisors of 8250?

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 8250 by each of the numbers from 1 to 8250 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)

8250 / 1 = 8250 (the remainder is 0, so 1 is a divisor of 8250)
8250 / 2 = 4125 (the remainder is 0, so 2 is a divisor of 8250)
8250 / 3 = 2750 (the remainder is 0, so 3 is a divisor of 8250)
...
8250 / 8249 = 1.0001212268154 (the remainder is 1, so 8249 is not a divisor of 8250)
8250 / 8250 = 1 (the remainder is 0, so 8250 is a divisor of 8250)

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 8250 (i.e. 90.829510622925). 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 $\frac{N}{d} = D$ )

8250 / 1 = 8250 (the remainder is 0, so 1 and 8250 are divisors of 8250)
8250 / 2 = 4125 (the remainder is 0, so 2 and 4125 are divisors of 8250)
8250 / 3 = 2750 (the remainder is 0, so 3 and 2750 are divisors of 8250)
...
8250 / 89 = 92.696629213483 (the remainder is 62, so 89 is not a divisor of 8250)
8250 / 90 = 91.666666666667 (the remainder is 60, so 90 is not a divisor of 8250)