What are the divisors of 3911?

1, 3911

There is a total of 2 positive divisors.
The sum of these divisors is 3912.
The arithmetic mean is 1956.

2 odd divisors

1, 3911

How to compute the divisors of 3911?

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 3911 by each of the numbers from 1 to 3911 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)

3911 / 1 = 3911 (the remainder is 0, so 1 is a divisor of 3911)
3911 / 2 = 1955.5 (the remainder is 1, so 2 is not a divisor of 3911)
3911 / 3 = 1303.6666666667 (the remainder is 2, so 3 is not a divisor of 3911)
...
3911 / 3910 = 1.0002557544757 (the remainder is 1, so 3910 is not a divisor of 3911)
3911 / 3911 = 1 (the remainder is 0, so 3911 is a divisor of 3911)

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 3911 (i.e. 62.537988455018). 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 $\frac{N}{d} = D$ )

3911 / 1 = 3911 (the remainder is 0, so 1 and 3911 are divisors of 3911)
3911 / 2 = 1955.5 (the remainder is 1, so 2 is not a divisor of 3911)
3911 / 3 = 1303.6666666667 (the remainder is 2, so 3 is not a divisor of 3911)
...
3911 / 61 = 64.114754098361 (the remainder is 7, so 61 is not a divisor of 3911)
3911 / 62 = 63.08064516129 (the remainder is 5, so 62 is not a divisor of 3911)