What are the divisors of 3313?

1, 3313

There is a total of 2 positive divisors.
The sum of these divisors is 3314.
The arithmetic mean is 1657.

2 odd divisors

1, 3313

How to compute the divisors of 3313?

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 3313 by each of the numbers from 1 to 3313 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)

3313 / 1 = 3313 (the remainder is 0, so 1 is a divisor of 3313)
3313 / 2 = 1656.5 (the remainder is 1, so 2 is not a divisor of 3313)
3313 / 3 = 1104.3333333333 (the remainder is 1, so 3 is not a divisor of 3313)
...
3313 / 3312 = 1.0003019323671 (the remainder is 1, so 3312 is not a divisor of 3313)
3313 / 3313 = 1 (the remainder is 0, so 3313 is a divisor of 3313)

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 3313 (i.e. 57.558665724633). 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 $\frac{N}{d} = D$ )

3313 / 1 = 3313 (the remainder is 0, so 1 and 3313 are divisors of 3313)
3313 / 2 = 1656.5 (the remainder is 1, so 2 is not a divisor of 3313)
3313 / 3 = 1104.3333333333 (the remainder is 1, so 3 is not a divisor of 3313)
...
3313 / 56 = 59.160714285714 (the remainder is 9, so 56 is not a divisor of 3313)
3313 / 57 = 58.122807017544 (the remainder is 7, so 57 is not a divisor of 3313)