What are the divisors of 3824?

1, 2, 4, 8, 16, 239, 478, 956, 1912, 3824

There is a total of 10 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 744.

8 even divisors

2, 4, 8, 16, 478, 956, 1912, 3824

2 odd divisors

1, 239

How to compute the divisors of 3824?

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 3824 by each of the numbers from 1 to 3824 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)

3824 / 1 = 3824 (the remainder is 0, so 1 is a divisor of 3824)
3824 / 2 = 1912 (the remainder is 0, so 2 is a divisor of 3824)
3824 / 3 = 1274.6666666667 (the remainder is 2, so 3 is not a divisor of 3824)
...
3824 / 3823 = 1.0002615746796 (the remainder is 1, so 3823 is not a divisor of 3824)
3824 / 3824 = 1 (the remainder is 0, so 3824 is a divisor of 3824)

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 3824 (i.e. 61.838499334961). 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 $\frac{N}{d} = D$ )

3824 / 1 = 3824 (the remainder is 0, so 1 and 3824 are divisors of 3824)
3824 / 2 = 1912 (the remainder is 0, so 2 and 1912 are divisors of 3824)
3824 / 3 = 1274.6666666667 (the remainder is 2, so 3 is not a divisor of 3824)
...
3824 / 60 = 63.733333333333 (the remainder is 44, so 60 is not a divisor of 3824)
3824 / 61 = 62.688524590164 (the remainder is 42, so 61 is not a divisor of 3824)