What are the divisors of 3356?

1, 2, 4, 839, 1678, 3356

There is a total of 6 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 980.

4 even divisors

2, 4, 1678, 3356

2 odd divisors

1, 839

How to compute the divisors of 3356?

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 3356 by each of the numbers from 1 to 3356 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)

3356 / 1 = 3356 (the remainder is 0, so 1 is a divisor of 3356)
3356 / 2 = 1678 (the remainder is 0, so 2 is a divisor of 3356)
3356 / 3 = 1118.6666666667 (the remainder is 2, so 3 is not a divisor of 3356)
...
3356 / 3355 = 1.0002980625931 (the remainder is 1, so 3355 is not a divisor of 3356)
3356 / 3356 = 1 (the remainder is 0, so 3356 is a divisor of 3356)

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 3356 (i.e. 57.930993431841). 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 $\frac{N}{d} = D$ )

3356 / 1 = 3356 (the remainder is 0, so 1 and 3356 are divisors of 3356)
3356 / 2 = 1678 (the remainder is 0, so 2 and 1678 are divisors of 3356)
3356 / 3 = 1118.6666666667 (the remainder is 2, so 3 is not a divisor of 3356)
...
3356 / 56 = 59.928571428571 (the remainder is 52, so 56 is not a divisor of 3356)
3356 / 57 = 58.877192982456 (the remainder is 50, so 57 is not a divisor of 3356)