What are the divisors of 5181?

1, 3, 11, 33, 157, 471, 1727, 5181

There is a total of 8 positive divisors.
The sum of these divisors is 7584.
The arithmetic mean is 948.

8 odd divisors

1, 3, 11, 33, 157, 471, 1727, 5181

How to compute the divisors of 5181?

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 5181 by each of the numbers from 1 to 5181 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)

5181 / 1 = 5181 (the remainder is 0, so 1 is a divisor of 5181)
5181 / 2 = 2590.5 (the remainder is 1, so 2 is not a divisor of 5181)
5181 / 3 = 1727 (the remainder is 0, so 3 is a divisor of 5181)
...
5181 / 5180 = 1.0001930501931 (the remainder is 1, so 5180 is not a divisor of 5181)
5181 / 5181 = 1 (the remainder is 0, so 5181 is a divisor of 5181)

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 5181 (i.e. 71.979163651712). 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 $\frac{N}{d} = D$ )

5181 / 1 = 5181 (the remainder is 0, so 1 and 5181 are divisors of 5181)
5181 / 2 = 2590.5 (the remainder is 1, so 2 is not a divisor of 5181)
5181 / 3 = 1727 (the remainder is 0, so 3 and 1727 are divisors of 5181)
...
5181 / 70 = 74.014285714286 (the remainder is 1, so 70 is not a divisor of 5181)
5181 / 71 = 72.971830985915 (the remainder is 69, so 71 is not a divisor of 5181)