What are the divisors of 3311?

1, 7, 11, 43, 77, 301, 473, 3311

There is a total of 8 positive divisors.
The sum of these divisors is 4224.
The arithmetic mean is 528.

8 odd divisors

1, 7, 11, 43, 77, 301, 473, 3311

How to compute the divisors of 3311?

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 3311 by each of the numbers from 1 to 3311 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)

3311 / 1 = 3311 (the remainder is 0, so 1 is a divisor of 3311)
3311 / 2 = 1655.5 (the remainder is 1, so 2 is not a divisor of 3311)
3311 / 3 = 1103.6666666667 (the remainder is 2, so 3 is not a divisor of 3311)
...
3311 / 3310 = 1.0003021148036 (the remainder is 1, so 3310 is not a divisor of 3311)
3311 / 3311 = 1 (the remainder is 0, so 3311 is a divisor of 3311)

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 3311 (i.e. 57.541289523263). 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 $\frac{N}{d} = D$ )

3311 / 1 = 3311 (the remainder is 0, so 1 and 3311 are divisors of 3311)
3311 / 2 = 1655.5 (the remainder is 1, so 2 is not a divisor of 3311)
3311 / 3 = 1103.6666666667 (the remainder is 2, so 3 is not a divisor of 3311)
...
3311 / 56 = 59.125 (the remainder is 7, so 56 is not a divisor of 3311)
3311 / 57 = 58.087719298246 (the remainder is 5, so 57 is not a divisor of 3311)