What are the divisors of 3964?

1, 2, 4, 991, 1982, 3964

There is a total of 6 positive divisors.
The sum of these divisors is 6944.
The arithmetic mean is 1157.3333333333.

4 even divisors

2, 4, 1982, 3964

2 odd divisors

1, 991

How to compute the divisors of 3964?

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 3964 by each of the numbers from 1 to 3964 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)

3964 / 1 = 3964 (the remainder is 0, so 1 is a divisor of 3964)
3964 / 2 = 1982 (the remainder is 0, so 2 is a divisor of 3964)
3964 / 3 = 1321.3333333333 (the remainder is 1, so 3 is not a divisor of 3964)
...
3964 / 3963 = 1.0002523340903 (the remainder is 1, so 3963 is not a divisor of 3964)
3964 / 3964 = 1 (the remainder is 0, so 3964 is a divisor of 3964)

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 3964 (i.e. 62.960304954789). 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 $\frac{N}{d} = D$ )

3964 / 1 = 3964 (the remainder is 0, so 1 and 3964 are divisors of 3964)
3964 / 2 = 1982 (the remainder is 0, so 2 and 1982 are divisors of 3964)
3964 / 3 = 1321.3333333333 (the remainder is 1, so 3 is not a divisor of 3964)
...
3964 / 61 = 64.983606557377 (the remainder is 60, so 61 is not a divisor of 3964)
3964 / 62 = 63.935483870968 (the remainder is 58, so 62 is not a divisor of 3964)