What are the divisors of 3183?

1, 3, 1061, 3183

There is a total of 4 positive divisors.
The sum of these divisors is 4248.
The arithmetic mean is 1062.

4 odd divisors

1, 3, 1061, 3183

How to compute the divisors of 3183?

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 3183 by each of the numbers from 1 to 3183 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)

3183 / 1 = 3183 (the remainder is 0, so 1 is a divisor of 3183)
3183 / 2 = 1591.5 (the remainder is 1, so 2 is not a divisor of 3183)
3183 / 3 = 1061 (the remainder is 0, so 3 is a divisor of 3183)
...
3183 / 3182 = 1.0003142677561 (the remainder is 1, so 3182 is not a divisor of 3183)
3183 / 3183 = 1 (the remainder is 0, so 3183 is a divisor of 3183)

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 3183 (i.e. 56.418082207746). 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 $\frac{N}{d} = D$ )

3183 / 1 = 3183 (the remainder is 0, so 1 and 3183 are divisors of 3183)
3183 / 2 = 1591.5 (the remainder is 1, so 2 is not a divisor of 3183)
3183 / 3 = 1061 (the remainder is 0, so 3 and 1061 are divisors of 3183)
...
3183 / 55 = 57.872727272727 (the remainder is 48, so 55 is not a divisor of 3183)
3183 / 56 = 56.839285714286 (the remainder is 47, so 56 is not a divisor of 3183)