What are the divisors of 3349?

1, 17, 197, 3349

There is a total of 4 positive divisors.
The sum of these divisors is 3564.
The arithmetic mean is 891.

4 odd divisors

1, 17, 197, 3349

How to compute the divisors of 3349?

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 3349 by each of the numbers from 1 to 3349 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)

3349 / 1 = 3349 (the remainder is 0, so 1 is a divisor of 3349)
3349 / 2 = 1674.5 (the remainder is 1, so 2 is not a divisor of 3349)
3349 / 3 = 1116.3333333333 (the remainder is 1, so 3 is not a divisor of 3349)
...
3349 / 3348 = 1.0002986857826 (the remainder is 1, so 3348 is not a divisor of 3349)
3349 / 3349 = 1 (the remainder is 0, so 3349 is a divisor of 3349)

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 3349 (i.e. 57.870545184921). 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 $\frac{N}{d} = D$ )

3349 / 1 = 3349 (the remainder is 0, so 1 and 3349 are divisors of 3349)
3349 / 2 = 1674.5 (the remainder is 1, so 2 is not a divisor of 3349)
3349 / 3 = 1116.3333333333 (the remainder is 1, so 3 is not a divisor of 3349)
...
3349 / 56 = 59.803571428571 (the remainder is 45, so 56 is not a divisor of 3349)
3349 / 57 = 58.754385964912 (the remainder is 43, so 57 is not a divisor of 3349)