What are the divisors of 2409?

1, 3, 11, 33, 73, 219, 803, 2409

There is a total of 8 positive divisors.
The sum of these divisors is 3552.
The arithmetic mean is 444.

8 odd divisors

1, 3, 11, 33, 73, 219, 803, 2409

How to compute the divisors of 2409?

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 2409 by each of the numbers from 1 to 2409 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)

2409 / 1 = 2409 (the remainder is 0, so 1 is a divisor of 2409)
2409 / 2 = 1204.5 (the remainder is 1, so 2 is not a divisor of 2409)
2409 / 3 = 803 (the remainder is 0, so 3 is a divisor of 2409)
...
2409 / 2408 = 1.000415282392 (the remainder is 1, so 2408 is not a divisor of 2409)
2409 / 2409 = 1 (the remainder is 0, so 2409 is a divisor of 2409)

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 2409 (i.e. 49.081564767232). 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 $\frac{N}{d} = D$ )

2409 / 1 = 2409 (the remainder is 0, so 1 and 2409 are divisors of 2409)
2409 / 2 = 1204.5 (the remainder is 1, so 2 is not a divisor of 2409)
2409 / 3 = 803 (the remainder is 0, so 3 and 803 are divisors of 2409)
...
2409 / 48 = 50.1875 (the remainder is 9, so 48 is not a divisor of 2409)
2409 / 49 = 49.163265306122 (the remainder is 8, so 49 is not a divisor of 2409)