What are the divisors of 3888?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 243, 324, 432, 486, 648, 972, 1296, 1944, 3888

There is a total of 30 positive divisors.
The sum of these divisors is 11284.
The arithmetic mean is 376.13333333333.

24 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 36, 48, 54, 72, 108, 144, 162, 216, 324, 432, 486, 648, 972, 1296, 1944, 3888

6 odd divisors

1, 3, 9, 27, 81, 243

How to compute the divisors of 3888?

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 3888 by each of the numbers from 1 to 3888 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)

3888 / 1 = 3888 (the remainder is 0, so 1 is a divisor of 3888)
3888 / 2 = 1944 (the remainder is 0, so 2 is a divisor of 3888)
3888 / 3 = 1296 (the remainder is 0, so 3 is a divisor of 3888)
...
3888 / 3887 = 1.0002572678158 (the remainder is 1, so 3887 is not a divisor of 3888)
3888 / 3888 = 1 (the remainder is 0, so 3888 is a divisor of 3888)

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 3888 (i.e. 62.35382907248). 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 $\frac{N}{d} = D$ )

3888 / 1 = 3888 (the remainder is 0, so 1 and 3888 are divisors of 3888)
3888 / 2 = 1944 (the remainder is 0, so 2 and 1944 are divisors of 3888)
3888 / 3 = 1296 (the remainder is 0, so 3 and 1296 are divisors of 3888)
...
3888 / 61 = 63.737704918033 (the remainder is 45, so 61 is not a divisor of 3888)
3888 / 62 = 62.709677419355 (the remainder is 44, so 62 is not a divisor of 3888)