What are the divisors of 2488?

1, 2, 4, 8, 311, 622, 1244, 2488

There is a total of 8 positive divisors.
The sum of these divisors is 4680.
The arithmetic mean is 585.

6 even divisors

2, 4, 8, 622, 1244, 2488

2 odd divisors

1, 311

How to compute the divisors of 2488?

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 2488 by each of the numbers from 1 to 2488 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)

2488 / 1 = 2488 (the remainder is 0, so 1 is a divisor of 2488)
2488 / 2 = 1244 (the remainder is 0, so 2 is a divisor of 2488)
2488 / 3 = 829.33333333333 (the remainder is 1, so 3 is not a divisor of 2488)
...
2488 / 2487 = 1.0004020908725 (the remainder is 1, so 2487 is not a divisor of 2488)
2488 / 2488 = 1 (the remainder is 0, so 2488 is a divisor of 2488)

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 2488 (i.e. 49.87985565336). 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 $\frac{N}{d} = D$ )

2488 / 1 = 2488 (the remainder is 0, so 1 and 2488 are divisors of 2488)
2488 / 2 = 1244 (the remainder is 0, so 2 and 1244 are divisors of 2488)
2488 / 3 = 829.33333333333 (the remainder is 1, so 3 is not a divisor of 2488)
...
2488 / 48 = 51.833333333333 (the remainder is 40, so 48 is not a divisor of 2488)
2488 / 49 = 50.775510204082 (the remainder is 38, so 49 is not a divisor of 2488)