What are the divisors of 3187?

1, 3187

There is a total of 2 positive divisors.
The sum of these divisors is 3188.
The arithmetic mean is 1594.

2 odd divisors

1, 3187

How to compute the divisors of 3187?

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 3187 by each of the numbers from 1 to 3187 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)

3187 / 1 = 3187 (the remainder is 0, so 1 is a divisor of 3187)
3187 / 2 = 1593.5 (the remainder is 1, so 2 is not a divisor of 3187)
3187 / 3 = 1062.3333333333 (the remainder is 1, so 3 is not a divisor of 3187)
...
3187 / 3186 = 1.0003138731952 (the remainder is 1, so 3186 is not a divisor of 3187)
3187 / 3187 = 1 (the remainder is 0, so 3187 is a divisor of 3187)

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 3187 (i.e. 56.45352070509). 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 $\frac{N}{d} = D$ )

3187 / 1 = 3187 (the remainder is 0, so 1 and 3187 are divisors of 3187)
3187 / 2 = 1593.5 (the remainder is 1, so 2 is not a divisor of 3187)
3187 / 3 = 1062.3333333333 (the remainder is 1, so 3 is not a divisor of 3187)
...
3187 / 55 = 57.945454545455 (the remainder is 52, so 55 is not a divisor of 3187)
3187 / 56 = 56.910714285714 (the remainder is 51, so 56 is not a divisor of 3187)