What are the divisors of 3399?

1, 3, 11, 33, 103, 309, 1133, 3399

There is a total of 8 positive divisors.
The sum of these divisors is 4992.
The arithmetic mean is 624.

8 odd divisors

1, 3, 11, 33, 103, 309, 1133, 3399

How to compute the divisors of 3399?

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 3399 by each of the numbers from 1 to 3399 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)

3399 / 1 = 3399 (the remainder is 0, so 1 is a divisor of 3399)
3399 / 2 = 1699.5 (the remainder is 1, so 2 is not a divisor of 3399)
3399 / 3 = 1133 (the remainder is 0, so 3 is a divisor of 3399)
...
3399 / 3398 = 1.0002942907593 (the remainder is 1, so 3398 is not a divisor of 3399)
3399 / 3399 = 1 (the remainder is 0, so 3399 is a divisor of 3399)

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 3399 (i.e. 58.300943388594). 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 $\frac{N}{d} = D$ )

3399 / 1 = 3399 (the remainder is 0, so 1 and 3399 are divisors of 3399)
3399 / 2 = 1699.5 (the remainder is 1, so 2 is not a divisor of 3399)
3399 / 3 = 1133 (the remainder is 0, so 3 and 1133 are divisors of 3399)
...
3399 / 57 = 59.631578947368 (the remainder is 36, so 57 is not a divisor of 3399)
3399 / 58 = 58.603448275862 (the remainder is 35, so 58 is not a divisor of 3399)