What are the divisors of 5298?

1, 2, 3, 6, 883, 1766, 2649, 5298

There is a total of 8 positive divisors.
The sum of these divisors is 10608.
The arithmetic mean is 1326.

4 even divisors

2, 6, 1766, 5298

4 odd divisors

1, 3, 883, 2649

How to compute the divisors of 5298?

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 5298 by each of the numbers from 1 to 5298 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)

5298 / 1 = 5298 (the remainder is 0, so 1 is a divisor of 5298)
5298 / 2 = 2649 (the remainder is 0, so 2 is a divisor of 5298)
5298 / 3 = 1766 (the remainder is 0, so 3 is a divisor of 5298)
...
5298 / 5297 = 1.0001887861053 (the remainder is 1, so 5297 is not a divisor of 5298)
5298 / 5298 = 1 (the remainder is 0, so 5298 is a divisor of 5298)

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 5298 (i.e. 72.787361540311). 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 $\frac{N}{d} = D$ )

5298 / 1 = 5298 (the remainder is 0, so 1 and 5298 are divisors of 5298)
5298 / 2 = 2649 (the remainder is 0, so 2 and 2649 are divisors of 5298)
5298 / 3 = 1766 (the remainder is 0, so 3 and 1766 are divisors of 5298)
...
5298 / 71 = 74.619718309859 (the remainder is 44, so 71 is not a divisor of 5298)
5298 / 72 = 73.583333333333 (the remainder is 42, so 72 is not a divisor of 5298)