What are the divisors of 3887?

1, 13, 23, 169, 299, 3887

There is a total of 6 positive divisors.
The sum of these divisors is 4392.
The arithmetic mean is 732.

6 odd divisors

1, 13, 23, 169, 299, 3887

How to compute the divisors of 3887?

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 3887 by each of the numbers from 1 to 3887 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)

3887 / 1 = 3887 (the remainder is 0, so 1 is a divisor of 3887)
3887 / 2 = 1943.5 (the remainder is 1, so 2 is not a divisor of 3887)
3887 / 3 = 1295.6666666667 (the remainder is 2, so 3 is not a divisor of 3887)
...
3887 / 3886 = 1.0002573340196 (the remainder is 1, so 3886 is not a divisor of 3887)
3887 / 3887 = 1 (the remainder is 0, so 3887 is a divisor of 3887)

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 3887 (i.e. 62.345809803065). 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 $\frac{N}{d} = D$ )

3887 / 1 = 3887 (the remainder is 0, so 1 and 3887 are divisors of 3887)
3887 / 2 = 1943.5 (the remainder is 1, so 2 is not a divisor of 3887)
3887 / 3 = 1295.6666666667 (the remainder is 2, so 3 is not a divisor of 3887)
...
3887 / 61 = 63.72131147541 (the remainder is 44, so 61 is not a divisor of 3887)
3887 / 62 = 62.693548387097 (the remainder is 43, so 62 is not a divisor of 3887)