What are the divisors of 3319?

1, 3319

There is a total of 2 positive divisors.
The sum of these divisors is 3320.
The arithmetic mean is 1660.

2 odd divisors

1, 3319

How to compute the divisors of 3319?

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 3319 by each of the numbers from 1 to 3319 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)

3319 / 1 = 3319 (the remainder is 0, so 1 is a divisor of 3319)
3319 / 2 = 1659.5 (the remainder is 1, so 2 is not a divisor of 3319)
3319 / 3 = 1106.3333333333 (the remainder is 1, so 3 is not a divisor of 3319)
...
3319 / 3318 = 1.0003013863773 (the remainder is 1, so 3318 is not a divisor of 3319)
3319 / 3319 = 1 (the remainder is 0, so 3319 is a divisor of 3319)

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 3319 (i.e. 57.610762883336). 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 $\frac{N}{d} = D$ )

3319 / 1 = 3319 (the remainder is 0, so 1 and 3319 are divisors of 3319)
3319 / 2 = 1659.5 (the remainder is 1, so 2 is not a divisor of 3319)
3319 / 3 = 1106.3333333333 (the remainder is 1, so 3 is not a divisor of 3319)
...
3319 / 56 = 59.267857142857 (the remainder is 15, so 56 is not a divisor of 3319)
3319 / 57 = 58.228070175439 (the remainder is 13, so 57 is not a divisor of 3319)