What are the divisors of 3189?

1, 3, 1063, 3189

There is a total of 4 positive divisors.
The sum of these divisors is 4256.
The arithmetic mean is 1064.

4 odd divisors

1, 3, 1063, 3189

How to compute the divisors of 3189?

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 3189 by each of the numbers from 1 to 3189 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)

3189 / 1 = 3189 (the remainder is 0, so 1 is a divisor of 3189)
3189 / 2 = 1594.5 (the remainder is 1, so 2 is not a divisor of 3189)
3189 / 3 = 1063 (the remainder is 0, so 3 is a divisor of 3189)
...
3189 / 3188 = 1.0003136762861 (the remainder is 1, so 3188 is not a divisor of 3189)
3189 / 3189 = 1 (the remainder is 0, so 3189 is a divisor of 3189)

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 3189 (i.e. 56.471231613982). 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 $\frac{N}{d} = D$ )

3189 / 1 = 3189 (the remainder is 0, so 1 and 3189 are divisors of 3189)
3189 / 2 = 1594.5 (the remainder is 1, so 2 is not a divisor of 3189)
3189 / 3 = 1063 (the remainder is 0, so 3 and 1063 are divisors of 3189)
...
3189 / 55 = 57.981818181818 (the remainder is 54, so 55 is not a divisor of 3189)
3189 / 56 = 56.946428571429 (the remainder is 53, so 56 is not a divisor of 3189)