What are the divisors of 3296?

1, 2, 4, 8, 16, 32, 103, 206, 412, 824, 1648, 3296

There is a total of 12 positive divisors.
The sum of these divisors is 6552.
The arithmetic mean is 546.

10 even divisors

2, 4, 8, 16, 32, 206, 412, 824, 1648, 3296

2 odd divisors

1, 103

How to compute the divisors of 3296?

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 3296 by each of the numbers from 1 to 3296 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)

3296 / 1 = 3296 (the remainder is 0, so 1 is a divisor of 3296)
3296 / 2 = 1648 (the remainder is 0, so 2 is a divisor of 3296)
3296 / 3 = 1098.6666666667 (the remainder is 2, so 3 is not a divisor of 3296)
...
3296 / 3295 = 1.0003034901366 (the remainder is 1, so 3295 is not a divisor of 3296)
3296 / 3296 = 1 (the remainder is 0, so 3296 is a divisor of 3296)

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 3296 (i.e. 57.410800377629). 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 $\frac{N}{d} = D$ )

3296 / 1 = 3296 (the remainder is 0, so 1 and 3296 are divisors of 3296)
3296 / 2 = 1648 (the remainder is 0, so 2 and 1648 are divisors of 3296)
3296 / 3 = 1098.6666666667 (the remainder is 2, so 3 is not a divisor of 3296)
...
3296 / 56 = 58.857142857143 (the remainder is 48, so 56 is not a divisor of 3296)
3296 / 57 = 57.824561403509 (the remainder is 47, so 57 is not a divisor of 3296)