What are the divisors of 4728?

1, 2, 3, 4, 6, 8, 12, 24, 197, 394, 591, 788, 1182, 1576, 2364, 4728

There is a total of 16 positive divisors.
The sum of these divisors is 11880.
The arithmetic mean is 742.5.

12 even divisors

2, 4, 6, 8, 12, 24, 394, 788, 1182, 1576, 2364, 4728

4 odd divisors

1, 3, 197, 591

How to compute the divisors of 4728?

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 4728 by each of the numbers from 1 to 4728 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)

4728 / 1 = 4728 (the remainder is 0, so 1 is a divisor of 4728)
4728 / 2 = 2364 (the remainder is 0, so 2 is a divisor of 4728)
4728 / 3 = 1576 (the remainder is 0, so 3 is a divisor of 4728)
...
4728 / 4727 = 1.0002115506664 (the remainder is 1, so 4727 is not a divisor of 4728)
4728 / 4728 = 1 (the remainder is 0, so 4728 is a divisor of 4728)

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 4728 (i.e. 68.760453750684). 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 $\frac{N}{d} = D$ )

4728 / 1 = 4728 (the remainder is 0, so 1 and 4728 are divisors of 4728)
4728 / 2 = 2364 (the remainder is 0, so 2 and 2364 are divisors of 4728)
4728 / 3 = 1576 (the remainder is 0, so 3 and 1576 are divisors of 4728)
...
4728 / 67 = 70.567164179104 (the remainder is 38, so 67 is not a divisor of 4728)
4728 / 68 = 69.529411764706 (the remainder is 36, so 68 is not a divisor of 4728)