What are the divisors of 3362?

1, 2, 41, 82, 1681, 3362

There is a total of 6 positive divisors.
The sum of these divisors is 5169.
The arithmetic mean is 861.5.

3 even divisors

2, 82, 3362

3 odd divisors

1, 41, 1681

How to compute the divisors of 3362?

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 3362 by each of the numbers from 1 to 3362 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)

3362 / 1 = 3362 (the remainder is 0, so 1 is a divisor of 3362)
3362 / 2 = 1681 (the remainder is 0, so 2 is a divisor of 3362)
3362 / 3 = 1120.6666666667 (the remainder is 2, so 3 is not a divisor of 3362)
...
3362 / 3361 = 1.0002975304969 (the remainder is 1, so 3361 is not a divisor of 3362)
3362 / 3362 = 1 (the remainder is 0, so 3362 is a divisor of 3362)

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 3362 (i.e. 57.982756057297). 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 $\frac{N}{d} = D$ )

3362 / 1 = 3362 (the remainder is 0, so 1 and 3362 are divisors of 3362)
3362 / 2 = 1681 (the remainder is 0, so 2 and 1681 are divisors of 3362)
3362 / 3 = 1120.6666666667 (the remainder is 2, so 3 is not a divisor of 3362)
...
3362 / 56 = 60.035714285714 (the remainder is 2, so 56 is not a divisor of 3362)
3362 / 57 = 58.982456140351 (the remainder is 56, so 57 is not a divisor of 3362)