What are the divisors of 4788?

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 19, 21, 28, 36, 38, 42, 57, 63, 76, 84, 114, 126, 133, 171, 228, 252, 266, 342, 399, 532, 684, 798, 1197, 1596, 2394, 4788

There is a total of 36 positive divisors.
The sum of these divisors is 14560.
The arithmetic mean is 404.44444444444.

24 even divisors

2, 4, 6, 12, 14, 18, 28, 36, 38, 42, 76, 84, 114, 126, 228, 252, 266, 342, 532, 684, 798, 1596, 2394, 4788

12 odd divisors

1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 399, 1197

How to compute the divisors of 4788?

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 4788 by each of the numbers from 1 to 4788 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)

4788 / 1 = 4788 (the remainder is 0, so 1 is a divisor of 4788)
4788 / 2 = 2394 (the remainder is 0, so 2 is a divisor of 4788)
4788 / 3 = 1596 (the remainder is 0, so 3 is a divisor of 4788)
...
4788 / 4787 = 1.0002088991017 (the remainder is 1, so 4787 is not a divisor of 4788)
4788 / 4788 = 1 (the remainder is 0, so 4788 is a divisor of 4788)

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 4788 (i.e. 69.195375568025). 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 $\frac{N}{d} = D$ )

4788 / 1 = 4788 (the remainder is 0, so 1 and 4788 are divisors of 4788)
4788 / 2 = 2394 (the remainder is 0, so 2 and 2394 are divisors of 4788)
4788 / 3 = 1596 (the remainder is 0, so 3 and 1596 are divisors of 4788)
...
4788 / 68 = 70.411764705882 (the remainder is 28, so 68 is not a divisor of 4788)
4788 / 69 = 69.391304347826 (the remainder is 27, so 69 is not a divisor of 4788)