What are the divisors of 3983?

1, 7, 569, 3983

There is a total of 4 positive divisors.
The sum of these divisors is 4560.
The arithmetic mean is 1140.

4 odd divisors

1, 7, 569, 3983

How to compute the divisors of 3983?

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 3983 by each of the numbers from 1 to 3983 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)

3983 / 1 = 3983 (the remainder is 0, so 1 is a divisor of 3983)
3983 / 2 = 1991.5 (the remainder is 1, so 2 is not a divisor of 3983)
3983 / 3 = 1327.6666666667 (the remainder is 2, so 3 is not a divisor of 3983)
...
3983 / 3982 = 1.0002511300854 (the remainder is 1, so 3982 is not a divisor of 3983)
3983 / 3983 = 1 (the remainder is 0, so 3983 is a divisor of 3983)

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 3983 (i.e. 63.111013301959). 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 $\frac{N}{d} = D$ )

3983 / 1 = 3983 (the remainder is 0, so 1 and 3983 are divisors of 3983)
3983 / 2 = 1991.5 (the remainder is 1, so 2 is not a divisor of 3983)
3983 / 3 = 1327.6666666667 (the remainder is 2, so 3 is not a divisor of 3983)
...
3983 / 62 = 64.241935483871 (the remainder is 15, so 62 is not a divisor of 3983)
3983 / 63 = 63.222222222222 (the remainder is 14, so 63 is not a divisor of 3983)