What are the divisors of 3323?

1, 3323

There is a total of 2 positive divisors.
The sum of these divisors is 3324.
The arithmetic mean is 1662.

2 odd divisors

1, 3323

How to compute the divisors of 3323?

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 3323 by each of the numbers from 1 to 3323 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)

3323 / 1 = 3323 (the remainder is 0, so 1 is a divisor of 3323)
3323 / 2 = 1661.5 (the remainder is 1, so 2 is not a divisor of 3323)
3323 / 3 = 1107.6666666667 (the remainder is 2, so 3 is not a divisor of 3323)
...
3323 / 3322 = 1.0003010234798 (the remainder is 1, so 3322 is not a divisor of 3323)
3323 / 3323 = 1 (the remainder is 0, so 3323 is a divisor of 3323)

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 3323 (i.e. 57.645468165329). 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 $\frac{N}{d} = D$ )

3323 / 1 = 3323 (the remainder is 0, so 1 and 3323 are divisors of 3323)
3323 / 2 = 1661.5 (the remainder is 1, so 2 is not a divisor of 3323)
3323 / 3 = 1107.6666666667 (the remainder is 2, so 3 is not a divisor of 3323)
...
3323 / 56 = 59.339285714286 (the remainder is 19, so 56 is not a divisor of 3323)
3323 / 57 = 58.298245614035 (the remainder is 17, so 57 is not a divisor of 3323)