What are the divisors of 3963?

1, 3, 1321, 3963

There is a total of 4 positive divisors.
The sum of these divisors is 5288.
The arithmetic mean is 1322.

4 odd divisors

1, 3, 1321, 3963

How to compute the divisors of 3963?

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 3963 by each of the numbers from 1 to 3963 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)

3963 / 1 = 3963 (the remainder is 0, so 1 is a divisor of 3963)
3963 / 2 = 1981.5 (the remainder is 1, so 2 is not a divisor of 3963)
3963 / 3 = 1321 (the remainder is 0, so 3 is a divisor of 3963)
...
3963 / 3962 = 1.0002523977789 (the remainder is 1, so 3962 is not a divisor of 3963)
3963 / 3963 = 1 (the remainder is 0, so 3963 is a divisor of 3963)

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 3963 (i.e. 62.952362942149). 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 $\frac{N}{d} = D$ )

3963 / 1 = 3963 (the remainder is 0, so 1 and 3963 are divisors of 3963)
3963 / 2 = 1981.5 (the remainder is 1, so 2 is not a divisor of 3963)
3963 / 3 = 1321 (the remainder is 0, so 3 and 1321 are divisors of 3963)
...
3963 / 61 = 64.967213114754 (the remainder is 59, so 61 is not a divisor of 3963)
3963 / 62 = 63.91935483871 (the remainder is 57, so 62 is not a divisor of 3963)