What are the divisors of 3386?

1, 2, 1693, 3386

There is a total of 4 positive divisors.
The sum of these divisors is 5082.
The arithmetic mean is 1270.5.

2 even divisors

2, 3386

2 odd divisors

1, 1693

How to compute the divisors of 3386?

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 3386 by each of the numbers from 1 to 3386 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)

3386 / 1 = 3386 (the remainder is 0, so 1 is a divisor of 3386)
3386 / 2 = 1693 (the remainder is 0, so 2 is a divisor of 3386)
3386 / 3 = 1128.6666666667 (the remainder is 2, so 3 is not a divisor of 3386)
...
3386 / 3385 = 1.0002954209749 (the remainder is 1, so 3385 is not a divisor of 3386)
3386 / 3386 = 1 (the remainder is 0, so 3386 is a divisor of 3386)

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 3386 (i.e. 58.189346103905). 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 $\frac{N}{d} = D$ )

3386 / 1 = 3386 (the remainder is 0, so 1 and 3386 are divisors of 3386)
3386 / 2 = 1693 (the remainder is 0, so 2 and 1693 are divisors of 3386)
3386 / 3 = 1128.6666666667 (the remainder is 2, so 3 is not a divisor of 3386)
...
3386 / 57 = 59.40350877193 (the remainder is 23, so 57 is not a divisor of 3386)
3386 / 58 = 58.379310344828 (the remainder is 22, so 58 is not a divisor of 3386)