What are the divisors of 3338?

1, 2, 1669, 3338

There is a total of 4 positive divisors.
The sum of these divisors is 5010.
The arithmetic mean is 1252.5.

2 even divisors

2, 3338

2 odd divisors

1, 1669

How to compute the divisors of 3338?

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 3338 by each of the numbers from 1 to 3338 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)

3338 / 1 = 3338 (the remainder is 0, so 1 is a divisor of 3338)
3338 / 2 = 1669 (the remainder is 0, so 2 is a divisor of 3338)
3338 / 3 = 1112.6666666667 (the remainder is 2, so 3 is not a divisor of 3338)
...
3338 / 3337 = 1.0002996703626 (the remainder is 1, so 3337 is not a divisor of 3338)
3338 / 3338 = 1 (the remainder is 0, so 3338 is a divisor of 3338)

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 3338 (i.e. 57.775427302617). 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 $\frac{N}{d} = D$ )

3338 / 1 = 3338 (the remainder is 0, so 1 and 3338 are divisors of 3338)
3338 / 2 = 1669 (the remainder is 0, so 2 and 1669 are divisors of 3338)
3338 / 3 = 1112.6666666667 (the remainder is 2, so 3 is not a divisor of 3338)
...
3338 / 56 = 59.607142857143 (the remainder is 34, so 56 is not a divisor of 3338)
3338 / 57 = 58.561403508772 (the remainder is 32, so 57 is not a divisor of 3338)