What are the divisors of 3186?

1, 2, 3, 6, 9, 18, 27, 54, 59, 118, 177, 354, 531, 1062, 1593, 3186

There is a total of 16 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 450.

8 even divisors

2, 6, 18, 54, 118, 354, 1062, 3186

8 odd divisors

1, 3, 9, 27, 59, 177, 531, 1593

How to compute the divisors of 3186?

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 3186 by each of the numbers from 1 to 3186 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)

3186 / 1 = 3186 (the remainder is 0, so 1 is a divisor of 3186)
3186 / 2 = 1593 (the remainder is 0, so 2 is a divisor of 3186)
3186 / 3 = 1062 (the remainder is 0, so 3 is a divisor of 3186)
...
3186 / 3185 = 1.0003139717425 (the remainder is 1, so 3185 is not a divisor of 3186)
3186 / 3186 = 1 (the remainder is 0, so 3186 is a divisor of 3186)

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 3186 (i.e. 56.44466316668). 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 $\frac{N}{d} = D$ )

3186 / 1 = 3186 (the remainder is 0, so 1 and 3186 are divisors of 3186)
3186 / 2 = 1593 (the remainder is 0, so 2 and 1593 are divisors of 3186)
3186 / 3 = 1062 (the remainder is 0, so 3 and 1062 are divisors of 3186)
...
3186 / 55 = 57.927272727273 (the remainder is 51, so 55 is not a divisor of 3186)
3186 / 56 = 56.892857142857 (the remainder is 50, so 56 is not a divisor of 3186)