What are the divisors of 8288?

1, 2, 4, 7, 8, 14, 16, 28, 32, 37, 56, 74, 112, 148, 224, 259, 296, 518, 592, 1036, 1184, 2072, 4144, 8288

There is a total of 24 positive divisors.
The sum of these divisors is 19152.
The arithmetic mean is 798.

20 even divisors

2, 4, 8, 14, 16, 28, 32, 56, 74, 112, 148, 224, 296, 518, 592, 1036, 1184, 2072, 4144, 8288

4 odd divisors

1, 7, 37, 259

How to compute the divisors of 8288?

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 8288 by each of the numbers from 1 to 8288 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)

8288 / 1 = 8288 (the remainder is 0, so 1 is a divisor of 8288)
8288 / 2 = 4144 (the remainder is 0, so 2 is a divisor of 8288)
8288 / 3 = 2762.6666666667 (the remainder is 2, so 3 is not a divisor of 8288)
...
8288 / 8287 = 1.0001206709304 (the remainder is 1, so 8287 is not a divisor of 8288)
8288 / 8288 = 1 (the remainder is 0, so 8288 is a divisor of 8288)

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 8288 (i.e. 91.038453413928). 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 $\frac{N}{d} = D$ )

8288 / 1 = 8288 (the remainder is 0, so 1 and 8288 are divisors of 8288)
8288 / 2 = 4144 (the remainder is 0, so 2 and 4144 are divisors of 8288)
8288 / 3 = 2762.6666666667 (the remainder is 2, so 3 is not a divisor of 8288)
...
8288 / 90 = 92.088888888889 (the remainder is 8, so 90 is not a divisor of 8288)
8288 / 91 = 91.076923076923 (the remainder is 7, so 91 is not a divisor of 8288)