What are the divisors of 3823?

1, 3823

There is a total of 2 positive divisors.
The sum of these divisors is 3824.
The arithmetic mean is 1912.

2 odd divisors

1, 3823

How to compute the divisors of 3823?

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 3823 by each of the numbers from 1 to 3823 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)

3823 / 1 = 3823 (the remainder is 0, so 1 is a divisor of 3823)
3823 / 2 = 1911.5 (the remainder is 1, so 2 is not a divisor of 3823)
3823 / 3 = 1274.3333333333 (the remainder is 1, so 3 is not a divisor of 3823)
...
3823 / 3822 = 1.0002616431188 (the remainder is 1, so 3822 is not a divisor of 3823)
3823 / 3823 = 1 (the remainder is 0, so 3823 is a divisor of 3823)

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 3823 (i.e. 61.830413228443). 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 $\frac{N}{d} = D$ )

3823 / 1 = 3823 (the remainder is 0, so 1 and 3823 are divisors of 3823)
3823 / 2 = 1911.5 (the remainder is 1, so 2 is not a divisor of 3823)
3823 / 3 = 1274.3333333333 (the remainder is 1, so 3 is not a divisor of 3823)
...
3823 / 60 = 63.716666666667 (the remainder is 43, so 60 is not a divisor of 3823)
3823 / 61 = 62.672131147541 (the remainder is 41, so 61 is not a divisor of 3823)