What are the divisors of 3284?

1, 2, 4, 821, 1642, 3284

There is a total of 6 positive divisors.
The sum of these divisors is 5754.
The arithmetic mean is 959.

4 even divisors

2, 4, 1642, 3284

2 odd divisors

1, 821

How to compute the divisors of 3284?

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 3284 by each of the numbers from 1 to 3284 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)

3284 / 1 = 3284 (the remainder is 0, so 1 is a divisor of 3284)
3284 / 2 = 1642 (the remainder is 0, so 2 is a divisor of 3284)
3284 / 3 = 1094.6666666667 (the remainder is 2, so 3 is not a divisor of 3284)
...
3284 / 3283 = 1.0003045994517 (the remainder is 1, so 3283 is not a divisor of 3284)
3284 / 3284 = 1 (the remainder is 0, so 3284 is a divisor of 3284)

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 3284 (i.e. 57.306195127578). 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 $\frac{N}{d} = D$ )

3284 / 1 = 3284 (the remainder is 0, so 1 and 3284 are divisors of 3284)
3284 / 2 = 1642 (the remainder is 0, so 2 and 1642 are divisors of 3284)
3284 / 3 = 1094.6666666667 (the remainder is 2, so 3 is not a divisor of 3284)
...
3284 / 56 = 58.642857142857 (the remainder is 36, so 56 is not a divisor of 3284)
3284 / 57 = 57.614035087719 (the remainder is 35, so 57 is not a divisor of 3284)