What are the divisors of 4752?

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 33, 36, 44, 48, 54, 66, 72, 88, 99, 108, 132, 144, 176, 198, 216, 264, 297, 396, 432, 528, 594, 792, 1188, 1584, 2376, 4752

There is a total of 40 positive divisors.
The sum of these divisors is 14880.
The arithmetic mean is 372.

32 even divisors

2, 4, 6, 8, 12, 16, 18, 22, 24, 36, 44, 48, 54, 66, 72, 88, 108, 132, 144, 176, 198, 216, 264, 396, 432, 528, 594, 792, 1188, 1584, 2376, 4752

8 odd divisors

1, 3, 9, 11, 27, 33, 99, 297

How to compute the divisors of 4752?

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 4752 by each of the numbers from 1 to 4752 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)

4752 / 1 = 4752 (the remainder is 0, so 1 is a divisor of 4752)
4752 / 2 = 2376 (the remainder is 0, so 2 is a divisor of 4752)
4752 / 3 = 1584 (the remainder is 0, so 3 is a divisor of 4752)
...
4752 / 4751 = 1.0002104820038 (the remainder is 1, so 4751 is not a divisor of 4752)
4752 / 4752 = 1 (the remainder is 0, so 4752 is a divisor of 4752)

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 4752 (i.e. 68.934751758456). 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 $\frac{N}{d} = D$ )

4752 / 1 = 4752 (the remainder is 0, so 1 and 4752 are divisors of 4752)
4752 / 2 = 2376 (the remainder is 0, so 2 and 2376 are divisors of 4752)
4752 / 3 = 1584 (the remainder is 0, so 3 and 1584 are divisors of 4752)
...
4752 / 67 = 70.925373134328 (the remainder is 62, so 67 is not a divisor of 4752)
4752 / 68 = 69.882352941176 (the remainder is 60, so 68 is not a divisor of 4752)