What are the divisors of 4686?

1, 2, 3, 6, 11, 22, 33, 66, 71, 142, 213, 426, 781, 1562, 2343, 4686

There is a total of 16 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 648.

8 even divisors

2, 6, 22, 66, 142, 426, 1562, 4686

8 odd divisors

1, 3, 11, 33, 71, 213, 781, 2343

How to compute the divisors of 4686?

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 4686 by each of the numbers from 1 to 4686 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)

4686 / 1 = 4686 (the remainder is 0, so 1 is a divisor of 4686)
4686 / 2 = 2343 (the remainder is 0, so 2 is a divisor of 4686)
4686 / 3 = 1562 (the remainder is 0, so 3 is a divisor of 4686)
...
4686 / 4685 = 1.0002134471718 (the remainder is 1, so 4685 is not a divisor of 4686)
4686 / 4686 = 1 (the remainder is 0, so 4686 is a divisor of 4686)

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 4686 (i.e. 68.454364360499). 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 $\frac{N}{d} = D$ )

4686 / 1 = 4686 (the remainder is 0, so 1 and 4686 are divisors of 4686)
4686 / 2 = 2343 (the remainder is 0, so 2 and 2343 are divisors of 4686)
4686 / 3 = 1562 (the remainder is 0, so 3 and 1562 are divisors of 4686)
...
4686 / 67 = 69.940298507463 (the remainder is 63, so 67 is not a divisor of 4686)
4686 / 68 = 68.911764705882 (the remainder is 62, so 68 is not a divisor of 4686)