What are the divisors of 5290?

1, 2, 5, 10, 23, 46, 115, 230, 529, 1058, 2645, 5290

There is a total of 12 positive divisors.
The sum of these divisors is 9954.
The arithmetic mean is 829.5.

6 even divisors

2, 10, 46, 230, 1058, 5290

6 odd divisors

1, 5, 23, 115, 529, 2645

How to compute the divisors of 5290?

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 5290 by each of the numbers from 1 to 5290 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)

5290 / 1 = 5290 (the remainder is 0, so 1 is a divisor of 5290)
5290 / 2 = 2645 (the remainder is 0, so 2 is a divisor of 5290)
5290 / 3 = 1763.3333333333 (the remainder is 1, so 3 is not a divisor of 5290)
...
5290 / 5289 = 1.0001890716582 (the remainder is 1, so 5289 is not a divisor of 5290)
5290 / 5290 = 1 (the remainder is 0, so 5290 is a divisor of 5290)

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 5290 (i.e. 72.732386183873). 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 $\frac{N}{d} = D$ )

5290 / 1 = 5290 (the remainder is 0, so 1 and 5290 are divisors of 5290)
5290 / 2 = 2645 (the remainder is 0, so 2 and 2645 are divisors of 5290)
5290 / 3 = 1763.3333333333 (the remainder is 1, so 3 is not a divisor of 5290)
...
5290 / 71 = 74.507042253521 (the remainder is 36, so 71 is not a divisor of 5290)
5290 / 72 = 73.472222222222 (the remainder is 34, so 72 is not a divisor of 5290)