What are the divisors of 2816?

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 256, 352, 704, 1408, 2816

There is a total of 18 positive divisors.
The sum of these divisors is 6132.
The arithmetic mean is 340.66666666667.

16 even divisors

2, 4, 8, 16, 22, 32, 44, 64, 88, 128, 176, 256, 352, 704, 1408, 2816

2 odd divisors

1, 11

How to compute the divisors of 2816?

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 2816 by each of the numbers from 1 to 2816 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)

2816 / 1 = 2816 (the remainder is 0, so 1 is a divisor of 2816)
2816 / 2 = 1408 (the remainder is 0, so 2 is a divisor of 2816)
2816 / 3 = 938.66666666667 (the remainder is 2, so 3 is not a divisor of 2816)
...
2816 / 2815 = 1.0003552397869 (the remainder is 1, so 2815 is not a divisor of 2816)
2816 / 2816 = 1 (the remainder is 0, so 2816 is a divisor of 2816)

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 2816 (i.e. 53.065996645686). 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 $\frac{N}{d} = D$ )

2816 / 1 = 2816 (the remainder is 0, so 1 and 2816 are divisors of 2816)
2816 / 2 = 1408 (the remainder is 0, so 2 and 1408 are divisors of 2816)
2816 / 3 = 938.66666666667 (the remainder is 2, so 3 is not a divisor of 2816)
...
2816 / 52 = 54.153846153846 (the remainder is 8, so 52 is not a divisor of 2816)
2816 / 53 = 53.132075471698 (the remainder is 7, so 53 is not a divisor of 2816)