What are the divisors of 3987?

1, 3, 9, 443, 1329, 3987

There is a total of 6 positive divisors.
The sum of these divisors is 5772.
The arithmetic mean is 962.

6 odd divisors

1, 3, 9, 443, 1329, 3987

How to compute the divisors of 3987?

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 3987 by each of the numbers from 1 to 3987 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)

3987 / 1 = 3987 (the remainder is 0, so 1 is a divisor of 3987)
3987 / 2 = 1993.5 (the remainder is 1, so 2 is not a divisor of 3987)
3987 / 3 = 1329 (the remainder is 0, so 3 is a divisor of 3987)
...
3987 / 3986 = 1.0002508780733 (the remainder is 1, so 3986 is not a divisor of 3987)
3987 / 3987 = 1 (the remainder is 0, so 3987 is a divisor of 3987)

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 3987 (i.e. 63.142695539548). 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 $\frac{N}{d} = D$ )

3987 / 1 = 3987 (the remainder is 0, so 1 and 3987 are divisors of 3987)
3987 / 2 = 1993.5 (the remainder is 1, so 2 is not a divisor of 3987)
3987 / 3 = 1329 (the remainder is 0, so 3 and 1329 are divisors of 3987)
...
3987 / 62 = 64.306451612903 (the remainder is 19, so 62 is not a divisor of 3987)
3987 / 63 = 63.285714285714 (the remainder is 18, so 63 is not a divisor of 3987)