What are the divisors of 3256?

1, 2, 4, 8, 11, 22, 37, 44, 74, 88, 148, 296, 407, 814, 1628, 3256

There is a total of 16 positive divisors.
The sum of these divisors is 6840.
The arithmetic mean is 427.5.

12 even divisors

2, 4, 8, 22, 44, 74, 88, 148, 296, 814, 1628, 3256

4 odd divisors

1, 11, 37, 407

How to compute the divisors of 3256?

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 3256 by each of the numbers from 1 to 3256 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)

3256 / 1 = 3256 (the remainder is 0, so 1 is a divisor of 3256)
3256 / 2 = 1628 (the remainder is 0, so 2 is a divisor of 3256)
3256 / 3 = 1085.3333333333 (the remainder is 1, so 3 is not a divisor of 3256)
...
3256 / 3255 = 1.0003072196621 (the remainder is 1, so 3255 is not a divisor of 3256)
3256 / 3256 = 1 (the remainder is 0, so 3256 is a divisor of 3256)

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 3256 (i.e. 57.061370470748). 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 $\frac{N}{d} = D$ )

3256 / 1 = 3256 (the remainder is 0, so 1 and 3256 are divisors of 3256)
3256 / 2 = 1628 (the remainder is 0, so 2 and 1628 are divisors of 3256)
3256 / 3 = 1085.3333333333 (the remainder is 1, so 3 is not a divisor of 3256)
...
3256 / 56 = 58.142857142857 (the remainder is 8, so 56 is not a divisor of 3256)
3256 / 57 = 57.122807017544 (the remainder is 7, so 57 is not a divisor of 3256)