What are the divisors of 480?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480

There is a total of 24 positive divisors.
The sum of these divisors is 1512.
The arithmetic mean is 63.

20 even divisors

2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480

4 odd divisors

1, 3, 5, 15

How to compute the divisors of 480?

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 480 by each of the numbers from 1 to 480 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)

480 / 1 = 480 (the remainder is 0, so 1 is a divisor of 480)
480 / 2 = 240 (the remainder is 0, so 2 is a divisor of 480)
480 / 3 = 160 (the remainder is 0, so 3 is a divisor of 480)
...
480 / 479 = 1.0020876826722 (the remainder is 1, so 479 is not a divisor of 480)
480 / 480 = 1 (the remainder is 0, so 480 is a divisor of 480)

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 480 (i.e. 21.908902300207). 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 $\frac{N}{d} = D$ )

480 / 1 = 480 (the remainder is 0, so 1 and 480 are divisors of 480)
480 / 2 = 240 (the remainder is 0, so 2 and 240 are divisors of 480)
480 / 3 = 160 (the remainder is 0, so 3 and 160 are divisors of 480)
...
480 / 20 = 24 (the remainder is 0, so 20 and 24 are divisors of 480)
480 / 21 = 22.857142857143 (the remainder is 18, so 21 is not a divisor of 480)