What are the divisors of 3893?

1, 17, 229, 3893

There is a total of 4 positive divisors.
The sum of these divisors is 4140.
The arithmetic mean is 1035.

4 odd divisors

1, 17, 229, 3893

How to compute the divisors of 3893?

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 3893 by each of the numbers from 1 to 3893 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)

3893 / 1 = 3893 (the remainder is 0, so 1 is a divisor of 3893)
3893 / 2 = 1946.5 (the remainder is 1, so 2 is not a divisor of 3893)
3893 / 3 = 1297.6666666667 (the remainder is 2, so 3 is not a divisor of 3893)
...
3893 / 3892 = 1.0002569373073 (the remainder is 1, so 3892 is not a divisor of 3893)
3893 / 3893 = 1 (the remainder is 0, so 3893 is a divisor of 3893)

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 3893 (i.e. 62.393909959226). 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 $\frac{N}{d} = D$ )

3893 / 1 = 3893 (the remainder is 0, so 1 and 3893 are divisors of 3893)
3893 / 2 = 1946.5 (the remainder is 1, so 2 is not a divisor of 3893)
3893 / 3 = 1297.6666666667 (the remainder is 2, so 3 is not a divisor of 3893)
...
3893 / 61 = 63.819672131148 (the remainder is 50, so 61 is not a divisor of 3893)
3893 / 62 = 62.790322580645 (the remainder is 49, so 62 is not a divisor of 3893)