What are the divisors of 5163?

1, 3, 1721, 5163

There is a total of 4 positive divisors.
The sum of these divisors is 6888.
The arithmetic mean is 1722.

4 odd divisors

1, 3, 1721, 5163

How to compute the divisors of 5163?

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 5163 by each of the numbers from 1 to 5163 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)

5163 / 1 = 5163 (the remainder is 0, so 1 is a divisor of 5163)
5163 / 2 = 2581.5 (the remainder is 1, so 2 is not a divisor of 5163)
5163 / 3 = 1721 (the remainder is 0, so 3 is a divisor of 5163)
...
5163 / 5162 = 1.000193723363 (the remainder is 1, so 5162 is not a divisor of 5163)
5163 / 5163 = 1 (the remainder is 0, so 5163 is a divisor of 5163)

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 5163 (i.e. 71.854018676759). 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 $\frac{N}{d} = D$ )

5163 / 1 = 5163 (the remainder is 0, so 1 and 5163 are divisors of 5163)
5163 / 2 = 2581.5 (the remainder is 1, so 2 is not a divisor of 5163)
5163 / 3 = 1721 (the remainder is 0, so 3 and 1721 are divisors of 5163)
...
5163 / 70 = 73.757142857143 (the remainder is 53, so 70 is not a divisor of 5163)
5163 / 71 = 72.718309859155 (the remainder is 51, so 71 is not a divisor of 5163)