What are the divisors of 2504?

1, 2, 4, 8, 313, 626, 1252, 2504

There is a total of 8 positive divisors.
The sum of these divisors is 4710.
The arithmetic mean is 588.75.

6 even divisors

2, 4, 8, 626, 1252, 2504

2 odd divisors

1, 313

How to compute the divisors of 2504?

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 2504 by each of the numbers from 1 to 2504 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)

2504 / 1 = 2504 (the remainder is 0, so 1 is a divisor of 2504)
2504 / 2 = 1252 (the remainder is 0, so 2 is a divisor of 2504)
2504 / 3 = 834.66666666667 (the remainder is 2, so 3 is not a divisor of 2504)
...
2504 / 2503 = 1.0003995205753 (the remainder is 1, so 2503 is not a divisor of 2504)
2504 / 2504 = 1 (the remainder is 0, so 2504 is a divisor of 2504)

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 2504 (i.e. 50.039984012787). 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 $\frac{N}{d} = D$ )

2504 / 1 = 2504 (the remainder is 0, so 1 and 2504 are divisors of 2504)
2504 / 2 = 1252 (the remainder is 0, so 2 and 1252 are divisors of 2504)
2504 / 3 = 834.66666666667 (the remainder is 2, so 3 is not a divisor of 2504)
...
2504 / 49 = 51.102040816327 (the remainder is 5, so 49 is not a divisor of 2504)
2504 / 50 = 50.08 (the remainder is 4, so 50 is not a divisor of 2504)