What are the divisors of 3331?

1, 3331

There is a total of 2 positive divisors.
The sum of these divisors is 3332.
The arithmetic mean is 1666.

2 odd divisors

1, 3331

How to compute the divisors of 3331?

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 3331 by each of the numbers from 1 to 3331 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)

3331 / 1 = 3331 (the remainder is 0, so 1 is a divisor of 3331)
3331 / 2 = 1665.5 (the remainder is 1, so 2 is not a divisor of 3331)
3331 / 3 = 1110.3333333333 (the remainder is 1, so 3 is not a divisor of 3331)
...
3331 / 3330 = 1.0003003003003 (the remainder is 1, so 3330 is not a divisor of 3331)
3331 / 3331 = 1 (the remainder is 0, so 3331 is a divisor of 3331)

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 3331 (i.e. 57.714816122032). 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 $\frac{N}{d} = D$ )

3331 / 1 = 3331 (the remainder is 0, so 1 and 3331 are divisors of 3331)
3331 / 2 = 1665.5 (the remainder is 1, so 2 is not a divisor of 3331)
3331 / 3 = 1110.3333333333 (the remainder is 1, so 3 is not a divisor of 3331)
...
3331 / 56 = 59.482142857143 (the remainder is 27, so 56 is not a divisor of 3331)
3331 / 57 = 58.438596491228 (the remainder is 25, so 57 is not a divisor of 3331)