What are the divisors of 3282?

1, 2, 3, 6, 547, 1094, 1641, 3282

There is a total of 8 positive divisors.
The sum of these divisors is 6576.
The arithmetic mean is 822.

4 even divisors

2, 6, 1094, 3282

4 odd divisors

1, 3, 547, 1641

How to compute the divisors of 3282?

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 3282 by each of the numbers from 1 to 3282 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)

3282 / 1 = 3282 (the remainder is 0, so 1 is a divisor of 3282)
3282 / 2 = 1641 (the remainder is 0, so 2 is a divisor of 3282)
3282 / 3 = 1094 (the remainder is 0, so 3 is a divisor of 3282)
...
3282 / 3281 = 1.0003047851265 (the remainder is 1, so 3281 is not a divisor of 3282)
3282 / 3282 = 1 (the remainder is 0, so 3282 is a divisor of 3282)

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 3282 (i.e. 57.28874234961). 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 $\frac{N}{d} = D$ )

3282 / 1 = 3282 (the remainder is 0, so 1 and 3282 are divisors of 3282)
3282 / 2 = 1641 (the remainder is 0, so 2 and 1641 are divisors of 3282)
3282 / 3 = 1094 (the remainder is 0, so 3 and 1094 are divisors of 3282)
...
3282 / 56 = 58.607142857143 (the remainder is 34, so 56 is not a divisor of 3282)
3282 / 57 = 57.578947368421 (the remainder is 33, so 57 is not a divisor of 3282)