What are the divisors of 3994?

1, 2, 1997, 3994

There is a total of 4 positive divisors.
The sum of these divisors is 5994.
The arithmetic mean is 1498.5.

2 even divisors

2, 3994

2 odd divisors

1, 1997

How to compute the divisors of 3994?

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 3994 by each of the numbers from 1 to 3994 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)

3994 / 1 = 3994 (the remainder is 0, so 1 is a divisor of 3994)
3994 / 2 = 1997 (the remainder is 0, so 2 is a divisor of 3994)
3994 / 3 = 1331.3333333333 (the remainder is 1, so 3 is not a divisor of 3994)
...
3994 / 3993 = 1.000250438267 (the remainder is 1, so 3993 is not a divisor of 3994)
3994 / 3994 = 1 (the remainder is 0, so 3994 is a divisor of 3994)

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 3994 (i.e. 63.1981012373). 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 $\frac{N}{d} = D$ )

3994 / 1 = 3994 (the remainder is 0, so 1 and 3994 are divisors of 3994)
3994 / 2 = 1997 (the remainder is 0, so 2 and 1997 are divisors of 3994)
3994 / 3 = 1331.3333333333 (the remainder is 1, so 3 is not a divisor of 3994)
...
3994 / 62 = 64.41935483871 (the remainder is 26, so 62 is not a divisor of 3994)
3994 / 63 = 63.396825396825 (the remainder is 25, so 63 is not a divisor of 3994)