What are the divisors of 3287?

1, 19, 173, 3287

There is a total of 4 positive divisors.
The sum of these divisors is 3480.
The arithmetic mean is 870.

4 odd divisors

1, 19, 173, 3287

How to compute the divisors of 3287?

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 3287 by each of the numbers from 1 to 3287 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)

3287 / 1 = 3287 (the remainder is 0, so 1 is a divisor of 3287)
3287 / 2 = 1643.5 (the remainder is 1, so 2 is not a divisor of 3287)
3287 / 3 = 1095.6666666667 (the remainder is 2, so 3 is not a divisor of 3287)
...
3287 / 3286 = 1.0003043213634 (the remainder is 1, so 3286 is not a divisor of 3287)
3287 / 3287 = 1 (the remainder is 0, so 3287 is a divisor of 3287)

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 3287 (i.e. 57.332364332897). 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 $\frac{N}{d} = D$ )

3287 / 1 = 3287 (the remainder is 0, so 1 and 3287 are divisors of 3287)
3287 / 2 = 1643.5 (the remainder is 1, so 2 is not a divisor of 3287)
3287 / 3 = 1095.6666666667 (the remainder is 2, so 3 is not a divisor of 3287)
...
3287 / 56 = 58.696428571429 (the remainder is 39, so 56 is not a divisor of 3287)
3287 / 57 = 57.666666666667 (the remainder is 38, so 57 is not a divisor of 3287)