What are the divisors of 3828?

1, 2, 3, 4, 6, 11, 12, 22, 29, 33, 44, 58, 66, 87, 116, 132, 174, 319, 348, 638, 957, 1276, 1914, 3828

There is a total of 24 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 420.

16 even divisors

2, 4, 6, 12, 22, 44, 58, 66, 116, 132, 174, 348, 638, 1276, 1914, 3828

8 odd divisors

1, 3, 11, 29, 33, 87, 319, 957

How to compute the divisors of 3828?

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 3828 by each of the numbers from 1 to 3828 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)

3828 / 1 = 3828 (the remainder is 0, so 1 is a divisor of 3828)
3828 / 2 = 1914 (the remainder is 0, so 2 is a divisor of 3828)
3828 / 3 = 1276 (the remainder is 0, so 3 is a divisor of 3828)
...
3828 / 3827 = 1.0002613012804 (the remainder is 1, so 3827 is not a divisor of 3828)
3828 / 3828 = 1 (the remainder is 0, so 3828 is a divisor of 3828)

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 3828 (i.e. 61.870833193032). 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 $\frac{N}{d} = D$ )

3828 / 1 = 3828 (the remainder is 0, so 1 and 3828 are divisors of 3828)
3828 / 2 = 1914 (the remainder is 0, so 2 and 1914 are divisors of 3828)
3828 / 3 = 1276 (the remainder is 0, so 3 and 1276 are divisors of 3828)
...
3828 / 60 = 63.8 (the remainder is 48, so 60 is not a divisor of 3828)
3828 / 61 = 62.754098360656 (the remainder is 46, so 61 is not a divisor of 3828)