What are the divisors of 3819?

1, 3, 19, 57, 67, 201, 1273, 3819

There is a total of 8 positive divisors.
The sum of these divisors is 5440.
The arithmetic mean is 680.

8 odd divisors

1, 3, 19, 57, 67, 201, 1273, 3819

How to compute the divisors of 3819?

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 3819 by each of the numbers from 1 to 3819 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)

3819 / 1 = 3819 (the remainder is 0, so 1 is a divisor of 3819)
3819 / 2 = 1909.5 (the remainder is 1, so 2 is not a divisor of 3819)
3819 / 3 = 1273 (the remainder is 0, so 3 is a divisor of 3819)
...
3819 / 3818 = 1.0002619172342 (the remainder is 1, so 3818 is not a divisor of 3819)
3819 / 3819 = 1 (the remainder is 0, so 3819 is a divisor of 3819)

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 3819 (i.e. 61.798058221922). 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 $\frac{N}{d} = D$ )

3819 / 1 = 3819 (the remainder is 0, so 1 and 3819 are divisors of 3819)
3819 / 2 = 1909.5 (the remainder is 1, so 2 is not a divisor of 3819)
3819 / 3 = 1273 (the remainder is 0, so 3 and 1273 are divisors of 3819)
...
3819 / 60 = 63.65 (the remainder is 39, so 60 is not a divisor of 3819)
3819 / 61 = 62.606557377049 (the remainder is 37, so 61 is not a divisor of 3819)