What are the divisors of 3343?

1, 3343

There is a total of 2 positive divisors.
The sum of these divisors is 3344.
The arithmetic mean is 1672.

2 odd divisors

1, 3343

How to compute the divisors of 3343?

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 3343 by each of the numbers from 1 to 3343 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)

3343 / 1 = 3343 (the remainder is 0, so 1 is a divisor of 3343)
3343 / 2 = 1671.5 (the remainder is 1, so 2 is not a divisor of 3343)
3343 / 3 = 1114.3333333333 (the remainder is 1, so 3 is not a divisor of 3343)
...
3343 / 3342 = 1.0002992220227 (the remainder is 1, so 3342 is not a divisor of 3343)
3343 / 3343 = 1 (the remainder is 0, so 3343 is a divisor of 3343)

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 3343 (i.e. 57.818682101895). 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 $\frac{N}{d} = D$ )

3343 / 1 = 3343 (the remainder is 0, so 1 and 3343 are divisors of 3343)
3343 / 2 = 1671.5 (the remainder is 1, so 2 is not a divisor of 3343)
3343 / 3 = 1114.3333333333 (the remainder is 1, so 3 is not a divisor of 3343)
...
3343 / 56 = 59.696428571429 (the remainder is 39, so 56 is not a divisor of 3343)
3343 / 57 = 58.649122807018 (the remainder is 37, so 57 is not a divisor of 3343)