What are the divisors of 3839?

1, 11, 349, 3839

There is a total of 4 positive divisors.
The sum of these divisors is 4200.
The arithmetic mean is 1050.

4 odd divisors

1, 11, 349, 3839

How to compute the divisors of 3839?

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 3839 by each of the numbers from 1 to 3839 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)

3839 / 1 = 3839 (the remainder is 0, so 1 is a divisor of 3839)
3839 / 2 = 1919.5 (the remainder is 1, so 2 is not a divisor of 3839)
3839 / 3 = 1279.6666666667 (the remainder is 2, so 3 is not a divisor of 3839)
...
3839 / 3838 = 1.000260552371 (the remainder is 1, so 3838 is not a divisor of 3839)
3839 / 3839 = 1 (the remainder is 0, so 3839 is a divisor of 3839)

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 3839 (i.e. 61.959664298639). 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 $\frac{N}{d} = D$ )

3839 / 1 = 3839 (the remainder is 0, so 1 and 3839 are divisors of 3839)
3839 / 2 = 1919.5 (the remainder is 1, so 2 is not a divisor of 3839)
3839 / 3 = 1279.6666666667 (the remainder is 2, so 3 is not a divisor of 3839)
...
3839 / 60 = 63.983333333333 (the remainder is 59, so 60 is not a divisor of 3839)
3839 / 61 = 62.934426229508 (the remainder is 57, so 61 is not a divisor of 3839)