What are the divisors of 3188?

1, 2, 4, 797, 1594, 3188

There is a total of 6 positive divisors.
The sum of these divisors is 5586.
The arithmetic mean is 931.

4 even divisors

2, 4, 1594, 3188

2 odd divisors

1, 797

How to compute the divisors of 3188?

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 3188 by each of the numbers from 1 to 3188 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)

3188 / 1 = 3188 (the remainder is 0, so 1 is a divisor of 3188)
3188 / 2 = 1594 (the remainder is 0, so 2 is a divisor of 3188)
3188 / 3 = 1062.6666666667 (the remainder is 2, so 3 is not a divisor of 3188)
...
3188 / 3187 = 1.0003137747098 (the remainder is 1, so 3187 is not a divisor of 3188)
3188 / 3188 = 1 (the remainder is 0, so 3188 is a divisor of 3188)

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 3188 (i.e. 56.462376853972). 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 $\frac{N}{d} = D$ )

3188 / 1 = 3188 (the remainder is 0, so 1 and 3188 are divisors of 3188)
3188 / 2 = 1594 (the remainder is 0, so 2 and 1594 are divisors of 3188)
3188 / 3 = 1062.6666666667 (the remainder is 2, so 3 is not a divisor of 3188)
...
3188 / 55 = 57.963636363636 (the remainder is 53, so 55 is not a divisor of 3188)
3188 / 56 = 56.928571428571 (the remainder is 52, so 56 is not a divisor of 3188)