What are the divisors of 2448?

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51, 68, 72, 102, 136, 144, 153, 204, 272, 306, 408, 612, 816, 1224, 2448

There is a total of 30 positive divisors.
The sum of these divisors is 7254.
The arithmetic mean is 241.8.

24 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 34, 36, 48, 68, 72, 102, 136, 144, 204, 272, 306, 408, 612, 816, 1224, 2448

6 odd divisors

1, 3, 9, 17, 51, 153

How to compute the divisors of 2448?

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 2448 by each of the numbers from 1 to 2448 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)

2448 / 1 = 2448 (the remainder is 0, so 1 is a divisor of 2448)
2448 / 2 = 1224 (the remainder is 0, so 2 is a divisor of 2448)
2448 / 3 = 816 (the remainder is 0, so 3 is a divisor of 2448)
...
2448 / 2447 = 1.0004086636698 (the remainder is 1, so 2447 is not a divisor of 2448)
2448 / 2448 = 1 (the remainder is 0, so 2448 is a divisor of 2448)

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 2448 (i.e. 49.477267507412). 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 $\frac{N}{d} = D$ )

2448 / 1 = 2448 (the remainder is 0, so 1 and 2448 are divisors of 2448)
2448 / 2 = 1224 (the remainder is 0, so 2 and 1224 are divisors of 2448)
2448 / 3 = 816 (the remainder is 0, so 3 and 816 are divisors of 2448)
...
2448 / 48 = 51 (the remainder is 0, so 48 and 51 are divisors of 2448)
2448 / 49 = 49.959183673469 (the remainder is 47, so 49 is not a divisor of 2448)