What are the divisors of 3378?

1, 2, 3, 6, 563, 1126, 1689, 3378

There is a total of 8 positive divisors.
The sum of these divisors is 6768.
The arithmetic mean is 846.

4 even divisors

2, 6, 1126, 3378

4 odd divisors

1, 3, 563, 1689

How to compute the divisors of 3378?

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 3378 by each of the numbers from 1 to 3378 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)

3378 / 1 = 3378 (the remainder is 0, so 1 is a divisor of 3378)
3378 / 2 = 1689 (the remainder is 0, so 2 is a divisor of 3378)
3378 / 3 = 1126 (the remainder is 0, so 3 is a divisor of 3378)
...
3378 / 3377 = 1.0002961208173 (the remainder is 1, so 3377 is not a divisor of 3378)
3378 / 3378 = 1 (the remainder is 0, so 3378 is a divisor of 3378)

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 3378 (i.e. 58.120564346882). 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 $\frac{N}{d} = D$ )

3378 / 1 = 3378 (the remainder is 0, so 1 and 3378 are divisors of 3378)
3378 / 2 = 1689 (the remainder is 0, so 2 and 1689 are divisors of 3378)
3378 / 3 = 1126 (the remainder is 0, so 3 and 1126 are divisors of 3378)
...
3378 / 57 = 59.263157894737 (the remainder is 15, so 57 is not a divisor of 3378)
3378 / 58 = 58.241379310345 (the remainder is 14, so 58 is not a divisor of 3378)