What are the divisors of 3864?

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 23, 24, 28, 42, 46, 56, 69, 84, 92, 138, 161, 168, 184, 276, 322, 483, 552, 644, 966, 1288, 1932, 3864

There is a total of 32 positive divisors.
The sum of these divisors is 11520.
The arithmetic mean is 360.

24 even divisors

2, 4, 6, 8, 12, 14, 24, 28, 42, 46, 56, 84, 92, 138, 168, 184, 276, 322, 552, 644, 966, 1288, 1932, 3864

8 odd divisors

1, 3, 7, 21, 23, 69, 161, 483

How to compute the divisors of 3864?

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 3864 by each of the numbers from 1 to 3864 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)

3864 / 1 = 3864 (the remainder is 0, so 1 is a divisor of 3864)
3864 / 2 = 1932 (the remainder is 0, so 2 is a divisor of 3864)
3864 / 3 = 1288 (the remainder is 0, so 3 is a divisor of 3864)
...
3864 / 3863 = 1.0002588661662 (the remainder is 1, so 3863 is not a divisor of 3864)
3864 / 3864 = 1 (the remainder is 0, so 3864 is a divisor of 3864)

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 3864 (i.e. 62.16108107168). 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 $\frac{N}{d} = D$ )

3864 / 1 = 3864 (the remainder is 0, so 1 and 3864 are divisors of 3864)
3864 / 2 = 1932 (the remainder is 0, so 2 and 1932 are divisors of 3864)
3864 / 3 = 1288 (the remainder is 0, so 3 and 1288 are divisors of 3864)
...
3864 / 61 = 63.344262295082 (the remainder is 21, so 61 is not a divisor of 3864)
3864 / 62 = 62.322580645161 (the remainder is 20, so 62 is not a divisor of 3864)