What are the divisors of 3849?

1, 3, 1283, 3849

There is a total of 4 positive divisors.
The sum of these divisors is 5136.
The arithmetic mean is 1284.

4 odd divisors

1, 3, 1283, 3849

How to compute the divisors of 3849?

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 3849 by each of the numbers from 1 to 3849 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)

3849 / 1 = 3849 (the remainder is 0, so 1 is a divisor of 3849)
3849 / 2 = 1924.5 (the remainder is 1, so 2 is not a divisor of 3849)
3849 / 3 = 1283 (the remainder is 0, so 3 is a divisor of 3849)
...
3849 / 3848 = 1.0002598752599 (the remainder is 1, so 3848 is not a divisor of 3849)
3849 / 3849 = 1 (the remainder is 0, so 3849 is a divisor of 3849)

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 3849 (i.e. 62.040309476984). 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 $\frac{N}{d} = D$ )

3849 / 1 = 3849 (the remainder is 0, so 1 and 3849 are divisors of 3849)
3849 / 2 = 1924.5 (the remainder is 1, so 2 is not a divisor of 3849)
3849 / 3 = 1283 (the remainder is 0, so 3 and 1283 are divisors of 3849)
...
3849 / 61 = 63.098360655738 (the remainder is 6, so 61 is not a divisor of 3849)
3849 / 62 = 62.08064516129 (the remainder is 5, so 62 is not a divisor of 3849)