What are the divisors of 3789?

1, 3, 9, 421, 1263, 3789

There is a total of 6 positive divisors.
The sum of these divisors is 5486.
The arithmetic mean is 914.33333333333.

6 odd divisors

1, 3, 9, 421, 1263, 3789

How to compute the divisors of 3789?

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 3789 by each of the numbers from 1 to 3789 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)

3789 / 1 = 3789 (the remainder is 0, so 1 is a divisor of 3789)
3789 / 2 = 1894.5 (the remainder is 1, so 2 is not a divisor of 3789)
3789 / 3 = 1263 (the remainder is 0, so 3 is a divisor of 3789)
...
3789 / 3788 = 1.0002639915523 (the remainder is 1, so 3788 is not a divisor of 3789)
3789 / 3789 = 1 (the remainder is 0, so 3789 is a divisor of 3789)

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 3789 (i.e. 61.55485358605). 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 $\frac{N}{d} = D$ )

3789 / 1 = 3789 (the remainder is 0, so 1 and 3789 are divisors of 3789)
3789 / 2 = 1894.5 (the remainder is 1, so 2 is not a divisor of 3789)
3789 / 3 = 1263 (the remainder is 0, so 3 and 1263 are divisors of 3789)
...
3789 / 60 = 63.15 (the remainder is 9, so 60 is not a divisor of 3789)
3789 / 61 = 62.114754098361 (the remainder is 7, so 61 is not a divisor of 3789)