What are the divisors of 4844?

1, 2, 4, 7, 14, 28, 173, 346, 692, 1211, 2422, 4844

There is a total of 12 positive divisors.
The sum of these divisors is 9744.
The arithmetic mean is 812.

8 even divisors

2, 4, 14, 28, 346, 692, 2422, 4844

4 odd divisors

1, 7, 173, 1211

How to compute the divisors of 4844?

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 4844 by each of the numbers from 1 to 4844 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)

4844 / 1 = 4844 (the remainder is 0, so 1 is a divisor of 4844)
4844 / 2 = 2422 (the remainder is 0, so 2 is a divisor of 4844)
4844 / 3 = 1614.6666666667 (the remainder is 2, so 3 is not a divisor of 4844)
...
4844 / 4843 = 1.0002064835846 (the remainder is 1, so 4843 is not a divisor of 4844)
4844 / 4844 = 1 (the remainder is 0, so 4844 is a divisor of 4844)

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 4844 (i.e. 69.598850565221). 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 $\frac{N}{d} = D$ )

4844 / 1 = 4844 (the remainder is 0, so 1 and 4844 are divisors of 4844)
4844 / 2 = 2422 (the remainder is 0, so 2 and 2422 are divisors of 4844)
4844 / 3 = 1614.6666666667 (the remainder is 2, so 3 is not a divisor of 4844)
...
4844 / 68 = 71.235294117647 (the remainder is 16, so 68 is not a divisor of 4844)
4844 / 69 = 70.202898550725 (the remainder is 14, so 69 is not a divisor of 4844)