What are the divisors of 3426?

1, 2, 3, 6, 571, 1142, 1713, 3426

There is a total of 8 positive divisors.
The sum of these divisors is 6864.
The arithmetic mean is 858.

4 even divisors

2, 6, 1142, 3426

4 odd divisors

1, 3, 571, 1713

How to compute the divisors of 3426?

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 3426 by each of the numbers from 1 to 3426 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)

3426 / 1 = 3426 (the remainder is 0, so 1 is a divisor of 3426)
3426 / 2 = 1713 (the remainder is 0, so 2 is a divisor of 3426)
3426 / 3 = 1142 (the remainder is 0, so 3 is a divisor of 3426)
...
3426 / 3425 = 1.0002919708029 (the remainder is 1, so 3425 is not a divisor of 3426)
3426 / 3426 = 1 (the remainder is 0, so 3426 is a divisor of 3426)

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 3426 (i.e. 58.532042506648). 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 $\frac{N}{d} = D$ )

3426 / 1 = 3426 (the remainder is 0, so 1 and 3426 are divisors of 3426)
3426 / 2 = 1713 (the remainder is 0, so 2 and 1713 are divisors of 3426)
3426 / 3 = 1142 (the remainder is 0, so 3 and 1142 are divisors of 3426)
...
3426 / 57 = 60.105263157895 (the remainder is 6, so 57 is not a divisor of 3426)
3426 / 58 = 59.068965517241 (the remainder is 4, so 58 is not a divisor of 3426)