What are the divisors of 6163?

1, 6163

There is a total of 2 positive divisors.
The sum of these divisors is 6164.
The arithmetic mean is 3082.

2 odd divisors

1, 6163

How to compute the divisors of 6163?

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 6163 by each of the numbers from 1 to 6163 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)

6163 / 1 = 6163 (the remainder is 0, so 1 is a divisor of 6163)
6163 / 2 = 3081.5 (the remainder is 1, so 2 is not a divisor of 6163)
6163 / 3 = 2054.3333333333 (the remainder is 1, so 3 is not a divisor of 6163)
...
6163 / 6162 = 1.0001622849724 (the remainder is 1, so 6162 is not a divisor of 6163)
6163 / 6163 = 1 (the remainder is 0, so 6163 is a divisor of 6163)

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 6163 (i.e. 78.50477692472). 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 $\frac{N}{d} = D$ )

6163 / 1 = 6163 (the remainder is 0, so 1 and 6163 are divisors of 6163)
6163 / 2 = 3081.5 (the remainder is 1, so 2 is not a divisor of 6163)
6163 / 3 = 2054.3333333333 (the remainder is 1, so 3 is not a divisor of 6163)
...
6163 / 77 = 80.038961038961 (the remainder is 3, so 77 is not a divisor of 6163)
6163 / 78 = 79.012820512821 (the remainder is 1, so 78 is not a divisor of 6163)