What are the divisors of 5166?

1, 2, 3, 6, 7, 9, 14, 18, 21, 41, 42, 63, 82, 123, 126, 246, 287, 369, 574, 738, 861, 1722, 2583, 5166

There is a total of 24 positive divisors.
The sum of these divisors is 13104.
The arithmetic mean is 546.

12 even divisors

2, 6, 14, 18, 42, 82, 126, 246, 574, 738, 1722, 5166

12 odd divisors

1, 3, 7, 9, 21, 41, 63, 123, 287, 369, 861, 2583

How to compute the divisors of 5166?

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 5166 by each of the numbers from 1 to 5166 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)

5166 / 1 = 5166 (the remainder is 0, so 1 is a divisor of 5166)
5166 / 2 = 2583 (the remainder is 0, so 2 is a divisor of 5166)
5166 / 3 = 1722 (the remainder is 0, so 3 is a divisor of 5166)
...
5166 / 5165 = 1.0001936108422 (the remainder is 1, so 5165 is not a divisor of 5166)
5166 / 5166 = 1 (the remainder is 0, so 5166 is a divisor of 5166)

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 5166 (i.e. 71.874891304266). 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 $\frac{N}{d} = D$ )

5166 / 1 = 5166 (the remainder is 0, so 1 and 5166 are divisors of 5166)
5166 / 2 = 2583 (the remainder is 0, so 2 and 2583 are divisors of 5166)
5166 / 3 = 1722 (the remainder is 0, so 3 and 1722 are divisors of 5166)
...
5166 / 70 = 73.8 (the remainder is 56, so 70 is not a divisor of 5166)
5166 / 71 = 72.760563380282 (the remainder is 54, so 71 is not a divisor of 5166)