What are the divisors of 3843?

1, 3, 7, 9, 21, 61, 63, 183, 427, 549, 1281, 3843

There is a total of 12 positive divisors.
The sum of these divisors is 6448.
The arithmetic mean is 537.33333333333.

12 odd divisors

1, 3, 7, 9, 21, 61, 63, 183, 427, 549, 1281, 3843

How to compute the divisors of 3843?

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 3843 by each of the numbers from 1 to 3843 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)

3843 / 1 = 3843 (the remainder is 0, so 1 is a divisor of 3843)
3843 / 2 = 1921.5 (the remainder is 1, so 2 is not a divisor of 3843)
3843 / 3 = 1281 (the remainder is 0, so 3 is a divisor of 3843)
...
3843 / 3842 = 1.0002602811036 (the remainder is 1, so 3842 is not a divisor of 3843)
3843 / 3843 = 1 (the remainder is 0, so 3843 is a divisor of 3843)

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 3843 (i.e. 61.991934959315). 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 $\frac{N}{d} = D$ )

3843 / 1 = 3843 (the remainder is 0, so 1 and 3843 are divisors of 3843)
3843 / 2 = 1921.5 (the remainder is 1, so 2 is not a divisor of 3843)
3843 / 3 = 1281 (the remainder is 0, so 3 and 1281 are divisors of 3843)
...
3843 / 60 = 64.05 (the remainder is 3, so 60 is not a divisor of 3843)
3843 / 61 = 63 (the remainder is 0, so 61 and 63 are divisors of 3843)