What are the divisors of 5259?

1, 3, 1753, 5259

There is a total of 4 positive divisors.
The sum of these divisors is 7016.
The arithmetic mean is 1754.

4 odd divisors

1, 3, 1753, 5259

How to compute the divisors of 5259?

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 5259 by each of the numbers from 1 to 5259 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)

5259 / 1 = 5259 (the remainder is 0, so 1 is a divisor of 5259)
5259 / 2 = 2629.5 (the remainder is 1, so 2 is not a divisor of 5259)
5259 / 3 = 1753 (the remainder is 0, so 3 is a divisor of 5259)
...
5259 / 5258 = 1.0001901863827 (the remainder is 1, so 5258 is not a divisor of 5259)
5259 / 5259 = 1 (the remainder is 0, so 5259 is a divisor of 5259)

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 5259 (i.e. 72.518963037264). 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 $\frac{N}{d} = D$ )

5259 / 1 = 5259 (the remainder is 0, so 1 and 5259 are divisors of 5259)
5259 / 2 = 2629.5 (the remainder is 1, so 2 is not a divisor of 5259)
5259 / 3 = 1753 (the remainder is 0, so 3 and 1753 are divisors of 5259)
...
5259 / 71 = 74.070422535211 (the remainder is 5, so 71 is not a divisor of 5259)
5259 / 72 = 73.041666666667 (the remainder is 3, so 72 is not a divisor of 5259)