What are the divisors of 2576?

1, 2, 4, 7, 8, 14, 16, 23, 28, 46, 56, 92, 112, 161, 184, 322, 368, 644, 1288, 2576

There is a total of 20 positive divisors.
The sum of these divisors is 5952.
The arithmetic mean is 297.6.

16 even divisors

2, 4, 8, 14, 16, 28, 46, 56, 92, 112, 184, 322, 368, 644, 1288, 2576

4 odd divisors

1, 7, 23, 161

How to compute the divisors of 2576?

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 2576 by each of the numbers from 1 to 2576 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)

2576 / 1 = 2576 (the remainder is 0, so 1 is a divisor of 2576)
2576 / 2 = 1288 (the remainder is 0, so 2 is a divisor of 2576)
2576 / 3 = 858.66666666667 (the remainder is 2, so 3 is not a divisor of 2576)
...
2576 / 2575 = 1.0003883495146 (the remainder is 1, so 2575 is not a divisor of 2576)
2576 / 2576 = 1 (the remainder is 0, so 2576 is a divisor of 2576)

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 2576 (i.e. 50.754310161798). 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 $\frac{N}{d} = D$ )

2576 / 1 = 2576 (the remainder is 0, so 1 and 2576 are divisors of 2576)
2576 / 2 = 1288 (the remainder is 0, so 2 and 1288 are divisors of 2576)
2576 / 3 = 858.66666666667 (the remainder is 2, so 3 is not a divisor of 2576)
...
2576 / 49 = 52.571428571429 (the remainder is 28, so 49 is not a divisor of 2576)
2576 / 50 = 51.52 (the remainder is 26, so 50 is not a divisor of 2576)