What are the divisors of 2487?

1, 3, 829, 2487

There is a total of 4 positive divisors.
The sum of these divisors is 3320.
The arithmetic mean is 830.

4 odd divisors

1, 3, 829, 2487

How to compute the divisors of 2487?

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 2487 by each of the numbers from 1 to 2487 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)

2487 / 1 = 2487 (the remainder is 0, so 1 is a divisor of 2487)
2487 / 2 = 1243.5 (the remainder is 1, so 2 is not a divisor of 2487)
2487 / 3 = 829 (the remainder is 0, so 3 is a divisor of 2487)
...
2487 / 2486 = 1.0004022526146 (the remainder is 1, so 2486 is not a divisor of 2487)
2487 / 2487 = 1 (the remainder is 0, so 2487 is a divisor of 2487)

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 2487 (i.e. 49.869830559167). 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 $\frac{N}{d} = D$ )

2487 / 1 = 2487 (the remainder is 0, so 1 and 2487 are divisors of 2487)
2487 / 2 = 1243.5 (the remainder is 1, so 2 is not a divisor of 2487)
2487 / 3 = 829 (the remainder is 0, so 3 and 829 are divisors of 2487)
...
2487 / 48 = 51.8125 (the remainder is 39, so 48 is not a divisor of 2487)
2487 / 49 = 50.755102040816 (the remainder is 37, so 49 is not a divisor of 2487)