What are the divisors of 3342?

1, 2, 3, 6, 557, 1114, 1671, 3342

There is a total of 8 positive divisors.
The sum of these divisors is 6696.
The arithmetic mean is 837.

4 even divisors

2, 6, 1114, 3342

4 odd divisors

1, 3, 557, 1671

How to compute the divisors of 3342?

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 3342 by each of the numbers from 1 to 3342 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)

3342 / 1 = 3342 (the remainder is 0, so 1 is a divisor of 3342)
3342 / 2 = 1671 (the remainder is 0, so 2 is a divisor of 3342)
3342 / 3 = 1114 (the remainder is 0, so 3 is a divisor of 3342)
...
3342 / 3341 = 1.0002993115834 (the remainder is 1, so 3341 is not a divisor of 3342)
3342 / 3342 = 1 (the remainder is 0, so 3342 is a divisor of 3342)

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 3342 (i.e. 57.810033731179). 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 $\frac{N}{d} = D$ )

3342 / 1 = 3342 (the remainder is 0, so 1 and 3342 are divisors of 3342)
3342 / 2 = 1671 (the remainder is 0, so 2 and 1671 are divisors of 3342)
3342 / 3 = 1114 (the remainder is 0, so 3 and 1114 are divisors of 3342)
...
3342 / 56 = 59.678571428571 (the remainder is 38, so 56 is not a divisor of 3342)
3342 / 57 = 58.631578947368 (the remainder is 36, so 57 is not a divisor of 3342)