What are the divisors of 3844?

1, 2, 4, 31, 62, 124, 961, 1922, 3844

There is a total of 9 positive divisors.
The sum of these divisors is 6951.
The arithmetic mean is 772.33333333333.

6 even divisors

2, 4, 62, 124, 1922, 3844

3 odd divisors

1, 31, 961

How to compute the divisors of 3844?

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 3844 by each of the numbers from 1 to 3844 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)

3844 / 1 = 3844 (the remainder is 0, so 1 is a divisor of 3844)
3844 / 2 = 1922 (the remainder is 0, so 2 is a divisor of 3844)
3844 / 3 = 1281.3333333333 (the remainder is 1, so 3 is not a divisor of 3844)
...
3844 / 3843 = 1.000260213375 (the remainder is 1, so 3843 is not a divisor of 3844)
3844 / 3844 = 1 (the remainder is 0, so 3844 is a divisor of 3844)

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 3844 (i.e. 62). 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 $\frac{N}{d} = D$ )

3844 / 1 = 3844 (the remainder is 0, so 1 and 3844 are divisors of 3844)
3844 / 2 = 1922 (the remainder is 0, so 2 and 1922 are divisors of 3844)
3844 / 3 = 1281.3333333333 (the remainder is 1, so 3 is not a divisor of 3844)
...
3844 / 61 = 63.016393442623 (the remainder is 1, so 61 is not a divisor of 3844)
3844 / 62 = 62 (the remainder is 0, so 62 and 62 are divisors of 3844)