What are the divisors of 3809?

1, 13, 293, 3809

There is a total of 4 positive divisors.
The sum of these divisors is 4116.
The arithmetic mean is 1029.

4 odd divisors

1, 13, 293, 3809

How to compute the divisors of 3809?

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 3809 by each of the numbers from 1 to 3809 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)

3809 / 1 = 3809 (the remainder is 0, so 1 is a divisor of 3809)
3809 / 2 = 1904.5 (the remainder is 1, so 2 is not a divisor of 3809)
3809 / 3 = 1269.6666666667 (the remainder is 2, so 3 is not a divisor of 3809)
...
3809 / 3808 = 1.000262605042 (the remainder is 1, so 3808 is not a divisor of 3809)
3809 / 3809 = 1 (the remainder is 0, so 3809 is a divisor of 3809)

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 3809 (i.e. 61.717096496838). 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 $\frac{N}{d} = D$ )

3809 / 1 = 3809 (the remainder is 0, so 1 and 3809 are divisors of 3809)
3809 / 2 = 1904.5 (the remainder is 1, so 2 is not a divisor of 3809)
3809 / 3 = 1269.6666666667 (the remainder is 2, so 3 is not a divisor of 3809)
...
3809 / 60 = 63.483333333333 (the remainder is 29, so 60 is not a divisor of 3809)
3809 / 61 = 62.44262295082 (the remainder is 27, so 61 is not a divisor of 3809)