What are the divisors of 3841?

1, 23, 167, 3841

There is a total of 4 positive divisors.
The sum of these divisors is 4032.
The arithmetic mean is 1008.

4 odd divisors

1, 23, 167, 3841

How to compute the divisors of 3841?

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 3841 by each of the numbers from 1 to 3841 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)

3841 / 1 = 3841 (the remainder is 0, so 1 is a divisor of 3841)
3841 / 2 = 1920.5 (the remainder is 1, so 2 is not a divisor of 3841)
3841 / 3 = 1280.3333333333 (the remainder is 1, so 3 is not a divisor of 3841)
...
3841 / 3840 = 1.0002604166667 (the remainder is 1, so 3840 is not a divisor of 3841)
3841 / 3841 = 1 (the remainder is 0, so 3841 is a divisor of 3841)

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 3841 (i.e. 61.975801729385). 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 $\frac{N}{d} = D$ )

3841 / 1 = 3841 (the remainder is 0, so 1 and 3841 are divisors of 3841)
3841 / 2 = 1920.5 (the remainder is 1, so 2 is not a divisor of 3841)
3841 / 3 = 1280.3333333333 (the remainder is 1, so 3 is not a divisor of 3841)
...
3841 / 60 = 64.016666666667 (the remainder is 1, so 60 is not a divisor of 3841)
3841 / 61 = 62.967213114754 (the remainder is 59, so 61 is not a divisor of 3841)