What are the divisors of 3831?

1, 3, 1277, 3831

There is a total of 4 positive divisors.
The sum of these divisors is 5112.
The arithmetic mean is 1278.

4 odd divisors

1, 3, 1277, 3831

How to compute the divisors of 3831?

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 3831 by each of the numbers from 1 to 3831 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)

3831 / 1 = 3831 (the remainder is 0, so 1 is a divisor of 3831)
3831 / 2 = 1915.5 (the remainder is 1, so 2 is not a divisor of 3831)
3831 / 3 = 1277 (the remainder is 0, so 3 is a divisor of 3831)
...
3831 / 3830 = 1.0002610966057 (the remainder is 1, so 3830 is not a divisor of 3831)
3831 / 3831 = 1 (the remainder is 0, so 3831 is a divisor of 3831)

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 3831 (i.e. 61.895072501775). 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 $\frac{N}{d} = D$ )

3831 / 1 = 3831 (the remainder is 0, so 1 and 3831 are divisors of 3831)
3831 / 2 = 1915.5 (the remainder is 1, so 2 is not a divisor of 3831)
3831 / 3 = 1277 (the remainder is 0, so 3 and 1277 are divisors of 3831)
...
3831 / 60 = 63.85 (the remainder is 51, so 60 is not a divisor of 3831)
3831 / 61 = 62.803278688525 (the remainder is 49, so 61 is not a divisor of 3831)