What are the divisors of 4848?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 101, 202, 303, 404, 606, 808, 1212, 1616, 2424, 4848

There is a total of 20 positive divisors.
The sum of these divisors is 12648.
The arithmetic mean is 632.4.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 202, 404, 606, 808, 1212, 1616, 2424, 4848

4 odd divisors

1, 3, 101, 303

How to compute the divisors of 4848?

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 4848 by each of the numbers from 1 to 4848 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)

4848 / 1 = 4848 (the remainder is 0, so 1 is a divisor of 4848)
4848 / 2 = 2424 (the remainder is 0, so 2 is a divisor of 4848)
4848 / 3 = 1616 (the remainder is 0, so 3 is a divisor of 4848)
...
4848 / 4847 = 1.0002063131834 (the remainder is 1, so 4847 is not a divisor of 4848)
4848 / 4848 = 1 (the remainder is 0, so 4848 is a divisor of 4848)

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 4848 (i.e. 69.627580742117). 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 $\frac{N}{d} = D$ )

4848 / 1 = 4848 (the remainder is 0, so 1 and 4848 are divisors of 4848)
4848 / 2 = 2424 (the remainder is 0, so 2 and 2424 are divisors of 4848)
4848 / 3 = 1616 (the remainder is 0, so 3 and 1616 are divisors of 4848)
...
4848 / 68 = 71.294117647059 (the remainder is 20, so 68 is not a divisor of 4848)
4848 / 69 = 70.260869565217 (the remainder is 18, so 69 is not a divisor of 4848)