What are the divisors of 3986?

1, 2, 1993, 3986

There is a total of 4 positive divisors.
The sum of these divisors is 5982.
The arithmetic mean is 1495.5.

2 even divisors

2, 3986

2 odd divisors

1, 1993

How to compute the divisors of 3986?

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 3986 by each of the numbers from 1 to 3986 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)

3986 / 1 = 3986 (the remainder is 0, so 1 is a divisor of 3986)
3986 / 2 = 1993 (the remainder is 0, so 2 is a divisor of 3986)
3986 / 3 = 1328.6666666667 (the remainder is 2, so 3 is not a divisor of 3986)
...
3986 / 3985 = 1.0002509410289 (the remainder is 1, so 3985 is not a divisor of 3986)
3986 / 3986 = 1 (the remainder is 0, so 3986 is a divisor of 3986)

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 3986 (i.e. 63.134776470658). 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 $\frac{N}{d} = D$ )

3986 / 1 = 3986 (the remainder is 0, so 1 and 3986 are divisors of 3986)
3986 / 2 = 1993 (the remainder is 0, so 2 and 1993 are divisors of 3986)
3986 / 3 = 1328.6666666667 (the remainder is 2, so 3 is not a divisor of 3986)
...
3986 / 62 = 64.290322580645 (the remainder is 18, so 62 is not a divisor of 3986)
3986 / 63 = 63.269841269841 (the remainder is 17, so 63 is not a divisor of 3986)