What are the divisors of 3244?

1, 2, 4, 811, 1622, 3244

There is a total of 6 positive divisors.
The sum of these divisors is 5684.
The arithmetic mean is 947.33333333333.

4 even divisors

2, 4, 1622, 3244

2 odd divisors

1, 811

How to compute the divisors of 3244?

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 3244 by each of the numbers from 1 to 3244 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)

3244 / 1 = 3244 (the remainder is 0, so 1 is a divisor of 3244)
3244 / 2 = 1622 (the remainder is 0, so 2 is a divisor of 3244)
3244 / 3 = 1081.3333333333 (the remainder is 1, so 3 is not a divisor of 3244)
...
3244 / 3243 = 1.0003083564601 (the remainder is 1, so 3243 is not a divisor of 3244)
3244 / 3244 = 1 (the remainder is 0, so 3244 is a divisor of 3244)

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 3244 (i.e. 56.956123463593). 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 $\frac{N}{d} = D$ )

3244 / 1 = 3244 (the remainder is 0, so 1 and 3244 are divisors of 3244)
3244 / 2 = 1622 (the remainder is 0, so 2 and 1622 are divisors of 3244)
3244 / 3 = 1081.3333333333 (the remainder is 1, so 3 is not a divisor of 3244)
...
3244 / 55 = 58.981818181818 (the remainder is 54, so 55 is not a divisor of 3244)
3244 / 56 = 57.928571428571 (the remainder is 52, so 56 is not a divisor of 3244)