What are the divisors of 3856?

1, 2, 4, 8, 16, 241, 482, 964, 1928, 3856

There is a total of 10 positive divisors.
The sum of these divisors is 7502.
The arithmetic mean is 750.2.

8 even divisors

2, 4, 8, 16, 482, 964, 1928, 3856

2 odd divisors

1, 241

How to compute the divisors of 3856?

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 3856 by each of the numbers from 1 to 3856 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)

3856 / 1 = 3856 (the remainder is 0, so 1 is a divisor of 3856)
3856 / 2 = 1928 (the remainder is 0, so 2 is a divisor of 3856)
3856 / 3 = 1285.3333333333 (the remainder is 1, so 3 is not a divisor of 3856)
...
3856 / 3855 = 1.0002594033722 (the remainder is 1, so 3855 is not a divisor of 3856)
3856 / 3856 = 1 (the remainder is 0, so 3856 is a divisor of 3856)

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 3856 (i.e. 62.09669878504). 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 $\frac{N}{d} = D$ )

3856 / 1 = 3856 (the remainder is 0, so 1 and 3856 are divisors of 3856)
3856 / 2 = 1928 (the remainder is 0, so 2 and 1928 are divisors of 3856)
3856 / 3 = 1285.3333333333 (the remainder is 1, so 3 is not a divisor of 3856)
...
3856 / 61 = 63.213114754098 (the remainder is 13, so 61 is not a divisor of 3856)
3856 / 62 = 62.193548387097 (the remainder is 12, so 62 is not a divisor of 3856)