What are the divisors of 5199?

1, 3, 1733, 5199

There is a total of 4 positive divisors.
The sum of these divisors is 6936.
The arithmetic mean is 1734.

4 odd divisors

1, 3, 1733, 5199

How to compute the divisors of 5199?

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 5199 by each of the numbers from 1 to 5199 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)

5199 / 1 = 5199 (the remainder is 0, so 1 is a divisor of 5199)
5199 / 2 = 2599.5 (the remainder is 1, so 2 is not a divisor of 5199)
5199 / 3 = 1733 (the remainder is 0, so 3 is a divisor of 5199)
...
5199 / 5198 = 1.0001923816853 (the remainder is 1, so 5198 is not a divisor of 5199)
5199 / 5199 = 1 (the remainder is 0, so 5199 is a divisor of 5199)

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 5199 (i.e. 72.104091423441). 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 $\frac{N}{d} = D$ )

5199 / 1 = 5199 (the remainder is 0, so 1 and 5199 are divisors of 5199)
5199 / 2 = 2599.5 (the remainder is 1, so 2 is not a divisor of 5199)
5199 / 3 = 1733 (the remainder is 0, so 3 and 1733 are divisors of 5199)
...
5199 / 71 = 73.225352112676 (the remainder is 16, so 71 is not a divisor of 5199)
5199 / 72 = 72.208333333333 (the remainder is 15, so 72 is not a divisor of 5199)