What are the divisors of 4800?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 150, 160, 192, 200, 240, 300, 320, 400, 480, 600, 800, 960, 1200, 1600, 2400, 4800

There is a total of 42 positive divisors.
The sum of these divisors is 15748.
The arithmetic mean is 374.95238095238.

36 even divisors

2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 32, 40, 48, 50, 60, 64, 80, 96, 100, 120, 150, 160, 192, 200, 240, 300, 320, 400, 480, 600, 800, 960, 1200, 1600, 2400, 4800

6 odd divisors

1, 3, 5, 15, 25, 75

How to compute the divisors of 4800?

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 4800 by each of the numbers from 1 to 4800 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)

4800 / 1 = 4800 (the remainder is 0, so 1 is a divisor of 4800)
4800 / 2 = 2400 (the remainder is 0, so 2 is a divisor of 4800)
4800 / 3 = 1600 (the remainder is 0, so 3 is a divisor of 4800)
...
4800 / 4799 = 1.0002083767452 (the remainder is 1, so 4799 is not a divisor of 4800)
4800 / 4800 = 1 (the remainder is 0, so 4800 is a divisor of 4800)

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 4800 (i.e. 69.282032302755). 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 $\frac{N}{d} = D$ )

4800 / 1 = 4800 (the remainder is 0, so 1 and 4800 are divisors of 4800)
4800 / 2 = 2400 (the remainder is 0, so 2 and 2400 are divisors of 4800)
4800 / 3 = 1600 (the remainder is 0, so 3 and 1600 are divisors of 4800)
...
4800 / 68 = 70.588235294118 (the remainder is 40, so 68 is not a divisor of 4800)
4800 / 69 = 69.565217391304 (the remainder is 39, so 69 is not a divisor of 4800)