What are the divisors of 5094?

1, 2, 3, 6, 9, 18, 283, 566, 849, 1698, 2547, 5094

There is a total of 12 positive divisors.
The sum of these divisors is 11076.
The arithmetic mean is 923.

6 even divisors

2, 6, 18, 566, 1698, 5094

6 odd divisors

1, 3, 9, 283, 849, 2547

How to compute the divisors of 5094?

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 5094 by each of the numbers from 1 to 5094 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)

5094 / 1 = 5094 (the remainder is 0, so 1 is a divisor of 5094)
5094 / 2 = 2547 (the remainder is 0, so 2 is a divisor of 5094)
5094 / 3 = 1698 (the remainder is 0, so 3 is a divisor of 5094)
...
5094 / 5093 = 1.0001963479285 (the remainder is 1, so 5093 is not a divisor of 5094)
5094 / 5094 = 1 (the remainder is 0, so 5094 is a divisor of 5094)

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 5094 (i.e. 71.372263520222). 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 $\frac{N}{d} = D$ )

5094 / 1 = 5094 (the remainder is 0, so 1 and 5094 are divisors of 5094)
5094 / 2 = 2547 (the remainder is 0, so 2 and 2547 are divisors of 5094)
5094 / 3 = 1698 (the remainder is 0, so 3 and 1698 are divisors of 5094)
...
5094 / 70 = 72.771428571429 (the remainder is 54, so 70 is not a divisor of 5094)
5094 / 71 = 71.746478873239 (the remainder is 53, so 71 is not a divisor of 5094)