What are the divisors of 4576?

1, 2, 4, 8, 11, 13, 16, 22, 26, 32, 44, 52, 88, 104, 143, 176, 208, 286, 352, 416, 572, 1144, 2288, 4576

There is a total of 24 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 441.

20 even divisors

2, 4, 8, 16, 22, 26, 32, 44, 52, 88, 104, 176, 208, 286, 352, 416, 572, 1144, 2288, 4576

4 odd divisors

1, 11, 13, 143

How to compute the divisors of 4576?

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 4576 by each of the numbers from 1 to 4576 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)

4576 / 1 = 4576 (the remainder is 0, so 1 is a divisor of 4576)
4576 / 2 = 2288 (the remainder is 0, so 2 is a divisor of 4576)
4576 / 3 = 1525.3333333333 (the remainder is 1, so 3 is not a divisor of 4576)
...
4576 / 4575 = 1.000218579235 (the remainder is 1, so 4575 is not a divisor of 4576)
4576 / 4576 = 1 (the remainder is 0, so 4576 is a divisor of 4576)

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 4576 (i.e. 67.646138101151). 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 $\frac{N}{d} = D$ )

4576 / 1 = 4576 (the remainder is 0, so 1 and 4576 are divisors of 4576)
4576 / 2 = 2288 (the remainder is 0, so 2 and 2288 are divisors of 4576)
4576 / 3 = 1525.3333333333 (the remainder is 1, so 3 is not a divisor of 4576)
...
4576 / 66 = 69.333333333333 (the remainder is 22, so 66 is not a divisor of 4576)
4576 / 67 = 68.298507462687 (the remainder is 20, so 67 is not a divisor of 4576)