What are the divisors of 3909?

1, 3, 1303, 3909

There is a total of 4 positive divisors.
The sum of these divisors is 5216.
The arithmetic mean is 1304.

4 odd divisors

1, 3, 1303, 3909

How to compute the divisors of 3909?

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 3909 by each of the numbers from 1 to 3909 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)

3909 / 1 = 3909 (the remainder is 0, so 1 is a divisor of 3909)
3909 / 2 = 1954.5 (the remainder is 1, so 2 is not a divisor of 3909)
3909 / 3 = 1303 (the remainder is 0, so 3 is a divisor of 3909)
...
3909 / 3908 = 1.0002558853634 (the remainder is 1, so 3908 is not a divisor of 3909)
3909 / 3909 = 1 (the remainder is 0, so 3909 is a divisor of 3909)

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 3909 (i.e. 62.521996129362). 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 $\frac{N}{d} = D$ )

3909 / 1 = 3909 (the remainder is 0, so 1 and 3909 are divisors of 3909)
3909 / 2 = 1954.5 (the remainder is 1, so 2 is not a divisor of 3909)
3909 / 3 = 1303 (the remainder is 0, so 3 and 1303 are divisors of 3909)
...
3909 / 61 = 64.081967213115 (the remainder is 5, so 61 is not a divisor of 3909)
3909 / 62 = 63.048387096774 (the remainder is 3, so 62 is not a divisor of 3909)