What are the divisors of 4842?

1, 2, 3, 6, 9, 18, 269, 538, 807, 1614, 2421, 4842

There is a total of 12 positive divisors.
The sum of these divisors is 10530.
The arithmetic mean is 877.5.

6 even divisors

2, 6, 18, 538, 1614, 4842

6 odd divisors

1, 3, 9, 269, 807, 2421

How to compute the divisors of 4842?

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 4842 by each of the numbers from 1 to 4842 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)

4842 / 1 = 4842 (the remainder is 0, so 1 is a divisor of 4842)
4842 / 2 = 2421 (the remainder is 0, so 2 is a divisor of 4842)
4842 / 3 = 1614 (the remainder is 0, so 3 is a divisor of 4842)
...
4842 / 4841 = 1.0002065688907 (the remainder is 1, so 4841 is not a divisor of 4842)
4842 / 4842 = 1 (the remainder is 0, so 4842 is a divisor of 4842)

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 4842 (i.e. 69.584481028459). 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 $\frac{N}{d} = D$ )

4842 / 1 = 4842 (the remainder is 0, so 1 and 4842 are divisors of 4842)
4842 / 2 = 2421 (the remainder is 0, so 2 and 2421 are divisors of 4842)
4842 / 3 = 1614 (the remainder is 0, so 3 and 1614 are divisors of 4842)
...
4842 / 68 = 71.205882352941 (the remainder is 14, so 68 is not a divisor of 4842)
4842 / 69 = 70.173913043478 (the remainder is 12, so 69 is not a divisor of 4842)