What are the divisors of 2518?

1, 2, 1259, 2518

There is a total of 4 positive divisors.
The sum of these divisors is 3780.
The arithmetic mean is 945.

2 even divisors

2, 2518

2 odd divisors

1, 1259

How to compute the divisors of 2518?

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 2518 by each of the numbers from 1 to 2518 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)

2518 / 1 = 2518 (the remainder is 0, so 1 is a divisor of 2518)
2518 / 2 = 1259 (the remainder is 0, so 2 is a divisor of 2518)
2518 / 3 = 839.33333333333 (the remainder is 1, so 3 is not a divisor of 2518)
...
2518 / 2517 = 1.0003972983711 (the remainder is 1, so 2517 is not a divisor of 2518)
2518 / 2518 = 1 (the remainder is 0, so 2518 is a divisor of 2518)

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 2518 (i.e. 50.179677161178). 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 $\frac{N}{d} = D$ )

2518 / 1 = 2518 (the remainder is 0, so 1 and 2518 are divisors of 2518)
2518 / 2 = 1259 (the remainder is 0, so 2 and 1259 are divisors of 2518)
2518 / 3 = 839.33333333333 (the remainder is 1, so 3 is not a divisor of 2518)
...
2518 / 49 = 51.387755102041 (the remainder is 19, so 49 is not a divisor of 2518)
2518 / 50 = 50.36 (the remainder is 18, so 50 is not a divisor of 2518)