What are the divisors of 3941?

1, 7, 563, 3941

There is a total of 4 positive divisors.
The sum of these divisors is 4512.
The arithmetic mean is 1128.

4 odd divisors

1, 7, 563, 3941

How to compute the divisors of 3941?

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 3941 by each of the numbers from 1 to 3941 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)

3941 / 1 = 3941 (the remainder is 0, so 1 is a divisor of 3941)
3941 / 2 = 1970.5 (the remainder is 1, so 2 is not a divisor of 3941)
3941 / 3 = 1313.6666666667 (the remainder is 2, so 3 is not a divisor of 3941)
...
3941 / 3940 = 1.0002538071066 (the remainder is 1, so 3940 is not a divisor of 3941)
3941 / 3941 = 1 (the remainder is 0, so 3941 is a divisor of 3941)

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 3941 (i.e. 62.777384462878). 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 $\frac{N}{d} = D$ )

3941 / 1 = 3941 (the remainder is 0, so 1 and 3941 are divisors of 3941)
3941 / 2 = 1970.5 (the remainder is 1, so 2 is not a divisor of 3941)
3941 / 3 = 1313.6666666667 (the remainder is 2, so 3 is not a divisor of 3941)
...
3941 / 61 = 64.606557377049 (the remainder is 37, so 61 is not a divisor of 3941)
3941 / 62 = 63.564516129032 (the remainder is 35, so 62 is not a divisor of 3941)