What are the divisors of 3268?

1, 2, 4, 19, 38, 43, 76, 86, 172, 817, 1634, 3268

There is a total of 12 positive divisors.
The sum of these divisors is 6160.
The arithmetic mean is 513.33333333333.

8 even divisors

2, 4, 38, 76, 86, 172, 1634, 3268

4 odd divisors

1, 19, 43, 817

How to compute the divisors of 3268?

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 3268 by each of the numbers from 1 to 3268 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)

3268 / 1 = 3268 (the remainder is 0, so 1 is a divisor of 3268)
3268 / 2 = 1634 (the remainder is 0, so 2 is a divisor of 3268)
3268 / 3 = 1089.3333333333 (the remainder is 1, so 3 is not a divisor of 3268)
...
3268 / 3267 = 1.0003060912152 (the remainder is 1, so 3267 is not a divisor of 3268)
3268 / 3268 = 1 (the remainder is 0, so 3268 is a divisor of 3268)

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 3268 (i.e. 57.166423711826). 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 $\frac{N}{d} = D$ )

3268 / 1 = 3268 (the remainder is 0, so 1 and 3268 are divisors of 3268)
3268 / 2 = 1634 (the remainder is 0, so 2 and 1634 are divisors of 3268)
3268 / 3 = 1089.3333333333 (the remainder is 1, so 3 is not a divisor of 3268)
...
3268 / 56 = 58.357142857143 (the remainder is 20, so 56 is not a divisor of 3268)
3268 / 57 = 57.333333333333 (the remainder is 19, so 57 is not a divisor of 3268)