What are the divisors of 3382?

1, 2, 19, 38, 89, 178, 1691, 3382

There is a total of 8 positive divisors.
The sum of these divisors is 5400.
The arithmetic mean is 675.

4 even divisors

2, 38, 178, 3382

4 odd divisors

1, 19, 89, 1691

How to compute the divisors of 3382?

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 3382 by each of the numbers from 1 to 3382 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)

3382 / 1 = 3382 (the remainder is 0, so 1 is a divisor of 3382)
3382 / 2 = 1691 (the remainder is 0, so 2 is a divisor of 3382)
3382 / 3 = 1127.3333333333 (the remainder is 1, so 3 is not a divisor of 3382)
...
3382 / 3381 = 1.0002957704821 (the remainder is 1, so 3381 is not a divisor of 3382)
3382 / 3382 = 1 (the remainder is 0, so 3382 is a divisor of 3382)

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 3382 (i.e. 58.154965394195). 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 $\frac{N}{d} = D$ )

3382 / 1 = 3382 (the remainder is 0, so 1 and 3382 are divisors of 3382)
3382 / 2 = 1691 (the remainder is 0, so 2 and 1691 are divisors of 3382)
3382 / 3 = 1127.3333333333 (the remainder is 1, so 3 is not a divisor of 3382)
...
3382 / 57 = 59.333333333333 (the remainder is 19, so 57 is not a divisor of 3382)
3382 / 58 = 58.310344827586 (the remainder is 18, so 58 is not a divisor of 3382)