What are the divisors of 3163?

1, 3163

There is a total of 2 positive divisors.
The sum of these divisors is 3164.
The arithmetic mean is 1582.

2 odd divisors

1, 3163

How to compute the divisors of 3163?

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 3163 by each of the numbers from 1 to 3163 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)

3163 / 1 = 3163 (the remainder is 0, so 1 is a divisor of 3163)
3163 / 2 = 1581.5 (the remainder is 1, so 2 is not a divisor of 3163)
3163 / 3 = 1054.3333333333 (the remainder is 1, so 3 is not a divisor of 3163)
...
3163 / 3162 = 1.0003162555345 (the remainder is 1, so 3162 is not a divisor of 3163)
3163 / 3163 = 1 (the remainder is 0, so 3163 is a divisor of 3163)

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 3163 (i.e. 56.240554762555). 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 $\frac{N}{d} = D$ )

3163 / 1 = 3163 (the remainder is 0, so 1 and 3163 are divisors of 3163)
3163 / 2 = 1581.5 (the remainder is 1, so 2 is not a divisor of 3163)
3163 / 3 = 1054.3333333333 (the remainder is 1, so 3 is not a divisor of 3163)
...
3163 / 55 = 57.509090909091 (the remainder is 28, so 55 is not a divisor of 3163)
3163 / 56 = 56.482142857143 (the remainder is 27, so 56 is not a divisor of 3163)