What are the divisors of 4839?

1, 3, 1613, 4839

There is a total of 4 positive divisors.
The sum of these divisors is 6456.
The arithmetic mean is 1614.

4 odd divisors

1, 3, 1613, 4839

How to compute the divisors of 4839?

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 4839 by each of the numbers from 1 to 4839 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)

4839 / 1 = 4839 (the remainder is 0, so 1 is a divisor of 4839)
4839 / 2 = 2419.5 (the remainder is 1, so 2 is not a divisor of 4839)
4839 / 3 = 1613 (the remainder is 0, so 3 is a divisor of 4839)
...
4839 / 4838 = 1.0002066969822 (the remainder is 1, so 4838 is not a divisor of 4839)
4839 / 4839 = 1 (the remainder is 0, so 4839 is a divisor of 4839)

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 4839 (i.e. 69.562921157755). 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 $\frac{N}{d} = D$ )

4839 / 1 = 4839 (the remainder is 0, so 1 and 4839 are divisors of 4839)
4839 / 2 = 2419.5 (the remainder is 1, so 2 is not a divisor of 4839)
4839 / 3 = 1613 (the remainder is 0, so 3 and 1613 are divisors of 4839)
...
4839 / 68 = 71.161764705882 (the remainder is 11, so 68 is not a divisor of 4839)
4839 / 69 = 70.130434782609 (the remainder is 9, so 69 is not a divisor of 4839)