What are the divisors of 5106?

1, 2, 3, 6, 23, 37, 46, 69, 74, 111, 138, 222, 851, 1702, 2553, 5106

There is a total of 16 positive divisors.
The sum of these divisors is 10944.
The arithmetic mean is 684.

8 even divisors

2, 6, 46, 74, 138, 222, 1702, 5106

8 odd divisors

1, 3, 23, 37, 69, 111, 851, 2553

How to compute the divisors of 5106?

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 5106 by each of the numbers from 1 to 5106 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)

5106 / 1 = 5106 (the remainder is 0, so 1 is a divisor of 5106)
5106 / 2 = 2553 (the remainder is 0, so 2 is a divisor of 5106)
5106 / 3 = 1702 (the remainder is 0, so 3 is a divisor of 5106)
...
5106 / 5105 = 1.0001958863859 (the remainder is 1, so 5105 is not a divisor of 5106)
5106 / 5106 = 1 (the remainder is 0, so 5106 is a divisor of 5106)

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 5106 (i.e. 71.456280339799). 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 $\frac{N}{d} = D$ )

5106 / 1 = 5106 (the remainder is 0, so 1 and 5106 are divisors of 5106)
5106 / 2 = 2553 (the remainder is 0, so 2 and 2553 are divisors of 5106)
5106 / 3 = 1702 (the remainder is 0, so 3 and 1702 are divisors of 5106)
...
5106 / 70 = 72.942857142857 (the remainder is 66, so 70 is not a divisor of 5106)
5106 / 71 = 71.915492957746 (the remainder is 65, so 71 is not a divisor of 5106)