What are the divisors of 3281?

1, 17, 193, 3281

There is a total of 4 positive divisors.
The sum of these divisors is 3492.
The arithmetic mean is 873.

4 odd divisors

1, 17, 193, 3281

How to compute the divisors of 3281?

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 3281 by each of the numbers from 1 to 3281 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)

3281 / 1 = 3281 (the remainder is 0, so 1 is a divisor of 3281)
3281 / 2 = 1640.5 (the remainder is 1, so 2 is not a divisor of 3281)
3281 / 3 = 1093.6666666667 (the remainder is 2, so 3 is not a divisor of 3281)
...
3281 / 3280 = 1.0003048780488 (the remainder is 1, so 3280 is not a divisor of 3281)
3281 / 3281 = 1 (the remainder is 0, so 3281 is a divisor of 3281)

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 3281 (i.e. 57.280013966479). 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 $\frac{N}{d} = D$ )

3281 / 1 = 3281 (the remainder is 0, so 1 and 3281 are divisors of 3281)
3281 / 2 = 1640.5 (the remainder is 1, so 2 is not a divisor of 3281)
3281 / 3 = 1093.6666666667 (the remainder is 2, so 3 is not a divisor of 3281)
...
3281 / 56 = 58.589285714286 (the remainder is 33, so 56 is not a divisor of 3281)
3281 / 57 = 57.561403508772 (the remainder is 32, so 57 is not a divisor of 3281)