What are the divisors of 2460?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 410, 492, 615, 820, 1230, 2460

There is a total of 24 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 294.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 82, 164, 246, 410, 492, 820, 1230, 2460

8 odd divisors

1, 3, 5, 15, 41, 123, 205, 615

How to compute the divisors of 2460?

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 2460 by each of the numbers from 1 to 2460 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)

2460 / 1 = 2460 (the remainder is 0, so 1 is a divisor of 2460)
2460 / 2 = 1230 (the remainder is 0, so 2 is a divisor of 2460)
2460 / 3 = 820 (the remainder is 0, so 3 is a divisor of 2460)
...
2460 / 2459 = 1.0004066693778 (the remainder is 1, so 2459 is not a divisor of 2460)
2460 / 2460 = 1 (the remainder is 0, so 2460 is a divisor of 2460)

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 2460 (i.e. 49.598387070549). 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 $\frac{N}{d} = D$ )

2460 / 1 = 2460 (the remainder is 0, so 1 and 2460 are divisors of 2460)
2460 / 2 = 1230 (the remainder is 0, so 2 and 1230 are divisors of 2460)
2460 / 3 = 820 (the remainder is 0, so 3 and 820 are divisors of 2460)
...
2460 / 48 = 51.25 (the remainder is 12, so 48 is not a divisor of 2460)
2460 / 49 = 50.204081632653 (the remainder is 10, so 49 is not a divisor of 2460)