What are the divisors of 3230?

1, 2, 5, 10, 17, 19, 34, 38, 85, 95, 170, 190, 323, 646, 1615, 3230

There is a total of 16 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 405.

8 even divisors

2, 10, 34, 38, 170, 190, 646, 3230

8 odd divisors

1, 5, 17, 19, 85, 95, 323, 1615

How to compute the divisors of 3230?

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 3230 by each of the numbers from 1 to 3230 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)

3230 / 1 = 3230 (the remainder is 0, so 1 is a divisor of 3230)
3230 / 2 = 1615 (the remainder is 0, so 2 is a divisor of 3230)
3230 / 3 = 1076.6666666667 (the remainder is 2, so 3 is not a divisor of 3230)
...
3230 / 3229 = 1.0003096934035 (the remainder is 1, so 3229 is not a divisor of 3230)
3230 / 3230 = 1 (the remainder is 0, so 3230 is a divisor of 3230)

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 3230 (i.e. 56.833088953531). 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 $\frac{N}{d} = D$ )

3230 / 1 = 3230 (the remainder is 0, so 1 and 3230 are divisors of 3230)
3230 / 2 = 1615 (the remainder is 0, so 2 and 1615 are divisors of 3230)
3230 / 3 = 1076.6666666667 (the remainder is 2, so 3 is not a divisor of 3230)
...
3230 / 55 = 58.727272727273 (the remainder is 40, so 55 is not a divisor of 3230)
3230 / 56 = 57.678571428571 (the remainder is 38, so 56 is not a divisor of 3230)