What are the divisors of 3406?

1, 2, 13, 26, 131, 262, 1703, 3406

There is a total of 8 positive divisors.
The sum of these divisors is 5544.
The arithmetic mean is 693.

4 even divisors

2, 26, 262, 3406

4 odd divisors

1, 13, 131, 1703

How to compute the divisors of 3406?

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 3406 by each of the numbers from 1 to 3406 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)

3406 / 1 = 3406 (the remainder is 0, so 1 is a divisor of 3406)
3406 / 2 = 1703 (the remainder is 0, so 2 is a divisor of 3406)
3406 / 3 = 1135.3333333333 (the remainder is 1, so 3 is not a divisor of 3406)
...
3406 / 3405 = 1.0002936857562 (the remainder is 1, so 3405 is not a divisor of 3406)
3406 / 3406 = 1 (the remainder is 0, so 3406 is a divisor of 3406)

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 3406 (i.e. 58.360945845659). 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 $\frac{N}{d} = D$ )

3406 / 1 = 3406 (the remainder is 0, so 1 and 3406 are divisors of 3406)
3406 / 2 = 1703 (the remainder is 0, so 2 and 1703 are divisors of 3406)
3406 / 3 = 1135.3333333333 (the remainder is 1, so 3 is not a divisor of 3406)
...
3406 / 57 = 59.754385964912 (the remainder is 43, so 57 is not a divisor of 3406)
3406 / 58 = 58.724137931034 (the remainder is 42, so 58 is not a divisor of 3406)