What are the divisors of 2472?

1, 2, 3, 4, 6, 8, 12, 24, 103, 206, 309, 412, 618, 824, 1236, 2472

There is a total of 16 positive divisors.
The sum of these divisors is 6240.
The arithmetic mean is 390.

12 even divisors

2, 4, 6, 8, 12, 24, 206, 412, 618, 824, 1236, 2472

4 odd divisors

1, 3, 103, 309

How to compute the divisors of 2472?

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 2472 by each of the numbers from 1 to 2472 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)

2472 / 1 = 2472 (the remainder is 0, so 1 is a divisor of 2472)
2472 / 2 = 1236 (the remainder is 0, so 2 is a divisor of 2472)
2472 / 3 = 824 (the remainder is 0, so 3 is a divisor of 2472)
...
2472 / 2471 = 1.0004046944557 (the remainder is 1, so 2471 is not a divisor of 2472)
2472 / 2472 = 1 (the remainder is 0, so 2472 is a divisor of 2472)

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 2472 (i.e. 49.719211578624). 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 $\frac{N}{d} = D$ )

2472 / 1 = 2472 (the remainder is 0, so 1 and 2472 are divisors of 2472)
2472 / 2 = 1236 (the remainder is 0, so 2 and 1236 are divisors of 2472)
2472 / 3 = 824 (the remainder is 0, so 3 and 824 are divisors of 2472)
...
2472 / 48 = 51.5 (the remainder is 24, so 48 is not a divisor of 2472)
2472 / 49 = 50.448979591837 (the remainder is 22, so 49 is not a divisor of 2472)