What are the divisors of 3944?

1, 2, 4, 8, 17, 29, 34, 58, 68, 116, 136, 232, 493, 986, 1972, 3944

There is a total of 16 positive divisors.
The sum of these divisors is 8100.
The arithmetic mean is 506.25.

12 even divisors

2, 4, 8, 34, 58, 68, 116, 136, 232, 986, 1972, 3944

4 odd divisors

1, 17, 29, 493

How to compute the divisors of 3944?

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 3944 by each of the numbers from 1 to 3944 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)

3944 / 1 = 3944 (the remainder is 0, so 1 is a divisor of 3944)
3944 / 2 = 1972 (the remainder is 0, so 2 is a divisor of 3944)
3944 / 3 = 1314.6666666667 (the remainder is 2, so 3 is not a divisor of 3944)
...
3944 / 3943 = 1.0002536139995 (the remainder is 1, so 3943 is not a divisor of 3944)
3944 / 3944 = 1 (the remainder is 0, so 3944 is a divisor of 3944)

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 3944 (i.e. 62.80127387243). 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 $\frac{N}{d} = D$ )

3944 / 1 = 3944 (the remainder is 0, so 1 and 3944 are divisors of 3944)
3944 / 2 = 1972 (the remainder is 0, so 2 and 1972 are divisors of 3944)
3944 / 3 = 1314.6666666667 (the remainder is 2, so 3 is not a divisor of 3944)
...
3944 / 61 = 64.655737704918 (the remainder is 40, so 61 is not a divisor of 3944)
3944 / 62 = 63.612903225806 (the remainder is 38, so 62 is not a divisor of 3944)