What are the divisors of 3943?

1, 3943

There is a total of 2 positive divisors.
The sum of these divisors is 3944.
The arithmetic mean is 1972.

2 odd divisors

1, 3943

How to compute the divisors of 3943?

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 3943 by each of the numbers from 1 to 3943 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)

3943 / 1 = 3943 (the remainder is 0, so 1 is a divisor of 3943)
3943 / 2 = 1971.5 (the remainder is 1, so 2 is not a divisor of 3943)
3943 / 3 = 1314.3333333333 (the remainder is 1, so 3 is not a divisor of 3943)
...
3943 / 3942 = 1.0002536783359 (the remainder is 1, so 3942 is not a divisor of 3943)
3943 / 3943 = 1 (the remainder is 0, so 3943 is a divisor of 3943)

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 3943 (i.e. 62.793311745758). 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 $\frac{N}{d} = D$ )

3943 / 1 = 3943 (the remainder is 0, so 1 and 3943 are divisors of 3943)
3943 / 2 = 1971.5 (the remainder is 1, so 2 is not a divisor of 3943)
3943 / 3 = 1314.3333333333 (the remainder is 1, so 3 is not a divisor of 3943)
...
3943 / 61 = 64.639344262295 (the remainder is 39, so 61 is not a divisor of 3943)
3943 / 62 = 63.596774193548 (the remainder is 37, so 62 is not a divisor of 3943)