What are the divisors of 2439?

1, 3, 9, 271, 813, 2439

There is a total of 6 positive divisors.
The sum of these divisors is 3536.
The arithmetic mean is 589.33333333333.

6 odd divisors

1, 3, 9, 271, 813, 2439

How to compute the divisors of 2439?

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 2439 by each of the numbers from 1 to 2439 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)

2439 / 1 = 2439 (the remainder is 0, so 1 is a divisor of 2439)
2439 / 2 = 1219.5 (the remainder is 1, so 2 is not a divisor of 2439)
2439 / 3 = 813 (the remainder is 0, so 3 is a divisor of 2439)
...
2439 / 2438 = 1.0004101722724 (the remainder is 1, so 2438 is not a divisor of 2439)
2439 / 2439 = 1 (the remainder is 0, so 2439 is a divisor of 2439)

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 2439 (i.e. 49.386232899463). 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 $\frac{N}{d} = D$ )

2439 / 1 = 2439 (the remainder is 0, so 1 and 2439 are divisors of 2439)
2439 / 2 = 1219.5 (the remainder is 1, so 2 is not a divisor of 2439)
2439 / 3 = 813 (the remainder is 0, so 3 and 813 are divisors of 2439)
...
2439 / 48 = 50.8125 (the remainder is 39, so 48 is not a divisor of 2439)
2439 / 49 = 49.775510204082 (the remainder is 38, so 49 is not a divisor of 2439)