What are the divisors of 3369?

1, 3, 1123, 3369

There is a total of 4 positive divisors.
The sum of these divisors is 4496.
The arithmetic mean is 1124.

4 odd divisors

1, 3, 1123, 3369

How to compute the divisors of 3369?

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 3369 by each of the numbers from 1 to 3369 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)

3369 / 1 = 3369 (the remainder is 0, so 1 is a divisor of 3369)
3369 / 2 = 1684.5 (the remainder is 1, so 2 is not a divisor of 3369)
3369 / 3 = 1123 (the remainder is 0, so 3 is a divisor of 3369)
...
3369 / 3368 = 1.000296912114 (the remainder is 1, so 3368 is not a divisor of 3369)
3369 / 3369 = 1 (the remainder is 0, so 3369 is a divisor of 3369)

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 3369 (i.e. 58.043087443726). 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 $\frac{N}{d} = D$ )

3369 / 1 = 3369 (the remainder is 0, so 1 and 3369 are divisors of 3369)
3369 / 2 = 1684.5 (the remainder is 1, so 2 is not a divisor of 3369)
3369 / 3 = 1123 (the remainder is 0, so 3 and 1123 are divisors of 3369)
...
3369 / 57 = 59.105263157895 (the remainder is 6, so 57 is not a divisor of 3369)
3369 / 58 = 58.086206896552 (the remainder is 5, so 58 is not a divisor of 3369)