What are the divisors of 6144?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 6144

There is a total of 24 positive divisors.
The sum of these divisors is 16380.
The arithmetic mean is 682.5.

22 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 6144

2 odd divisors

1, 3

How to compute the divisors of 6144?

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 6144 by each of the numbers from 1 to 6144 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)

6144 / 1 = 6144 (the remainder is 0, so 1 is a divisor of 6144)
6144 / 2 = 3072 (the remainder is 0, so 2 is a divisor of 6144)
6144 / 3 = 2048 (the remainder is 0, so 3 is a divisor of 6144)
...
6144 / 6143 = 1.0001627869119 (the remainder is 1, so 6143 is not a divisor of 6144)
6144 / 6144 = 1 (the remainder is 0, so 6144 is a divisor of 6144)

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 6144 (i.e. 78.383671769062). 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 $\frac{N}{d} = D$ )

6144 / 1 = 6144 (the remainder is 0, so 1 and 6144 are divisors of 6144)
6144 / 2 = 3072 (the remainder is 0, so 2 and 3072 are divisors of 6144)
6144 / 3 = 2048 (the remainder is 0, so 3 and 2048 are divisors of 6144)
...
6144 / 77 = 79.792207792208 (the remainder is 61, so 77 is not a divisor of 6144)
6144 / 78 = 78.769230769231 (the remainder is 60, so 78 is not a divisor of 6144)