What are the divisors of 3903?

1, 3, 1301, 3903

There is a total of 4 positive divisors.
The sum of these divisors is 5208.
The arithmetic mean is 1302.

4 odd divisors

1, 3, 1301, 3903

How to compute the divisors of 3903?

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 3903 by each of the numbers from 1 to 3903 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)

3903 / 1 = 3903 (the remainder is 0, so 1 is a divisor of 3903)
3903 / 2 = 1951.5 (the remainder is 1, so 2 is not a divisor of 3903)
3903 / 3 = 1301 (the remainder is 0, so 3 is a divisor of 3903)
...
3903 / 3902 = 1.0002562788314 (the remainder is 1, so 3902 is not a divisor of 3903)
3903 / 3903 = 1 (the remainder is 0, so 3903 is a divisor of 3903)

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 3903 (i.e. 62.473994589749). 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 $\frac{N}{d} = D$ )

3903 / 1 = 3903 (the remainder is 0, so 1 and 3903 are divisors of 3903)
3903 / 2 = 1951.5 (the remainder is 1, so 2 is not a divisor of 3903)
3903 / 3 = 1301 (the remainder is 0, so 3 and 1301 are divisors of 3903)
...
3903 / 61 = 63.983606557377 (the remainder is 60, so 61 is not a divisor of 3903)
3903 / 62 = 62.951612903226 (the remainder is 59, so 62 is not a divisor of 3903)