What are the divisors of 2463?

1, 3, 821, 2463

There is a total of 4 positive divisors.
The sum of these divisors is 3288.
The arithmetic mean is 822.

4 odd divisors

1, 3, 821, 2463

How to compute the divisors of 2463?

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 2463 by each of the numbers from 1 to 2463 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)

2463 / 1 = 2463 (the remainder is 0, so 1 is a divisor of 2463)
2463 / 2 = 1231.5 (the remainder is 1, so 2 is not a divisor of 2463)
2463 / 3 = 821 (the remainder is 0, so 3 is a divisor of 2463)
...
2463 / 2462 = 1.0004061738424 (the remainder is 1, so 2462 is not a divisor of 2463)
2463 / 2463 = 1 (the remainder is 0, so 2463 is a divisor of 2463)

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 2463 (i.e. 49.62862077471). 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 $\frac{N}{d} = D$ )

2463 / 1 = 2463 (the remainder is 0, so 1 and 2463 are divisors of 2463)
2463 / 2 = 1231.5 (the remainder is 1, so 2 is not a divisor of 2463)
2463 / 3 = 821 (the remainder is 0, so 3 and 821 are divisors of 2463)
...
2463 / 48 = 51.3125 (the remainder is 15, so 48 is not a divisor of 2463)
2463 / 49 = 50.265306122449 (the remainder is 13, so 49 is not a divisor of 2463)