What are the divisors of 3873?

1, 3, 1291, 3873

There is a total of 4 positive divisors.
The sum of these divisors is 5168.
The arithmetic mean is 1292.

4 odd divisors

1, 3, 1291, 3873

How to compute the divisors of 3873?

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 3873 by each of the numbers from 1 to 3873 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)

3873 / 1 = 3873 (the remainder is 0, so 1 is a divisor of 3873)
3873 / 2 = 1936.5 (the remainder is 1, so 2 is not a divisor of 3873)
3873 / 3 = 1291 (the remainder is 0, so 3 is a divisor of 3873)
...
3873 / 3872 = 1.0002582644628 (the remainder is 1, so 3872 is not a divisor of 3873)
3873 / 3873 = 1 (the remainder is 0, so 3873 is a divisor of 3873)

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 3873 (i.e. 62.233431530006). 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 $\frac{N}{d} = D$ )

3873 / 1 = 3873 (the remainder is 0, so 1 and 3873 are divisors of 3873)
3873 / 2 = 1936.5 (the remainder is 1, so 2 is not a divisor of 3873)
3873 / 3 = 1291 (the remainder is 0, so 3 and 1291 are divisors of 3873)
...
3873 / 61 = 63.491803278689 (the remainder is 30, so 61 is not a divisor of 3873)
3873 / 62 = 62.467741935484 (the remainder is 29, so 62 is not a divisor of 3873)