What are the divisors of 2512?

1, 2, 4, 8, 16, 157, 314, 628, 1256, 2512

There is a total of 10 positive divisors.
The sum of these divisors is 4898.
The arithmetic mean is 489.8.

8 even divisors

2, 4, 8, 16, 314, 628, 1256, 2512

2 odd divisors

1, 157

How to compute the divisors of 2512?

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 2512 by each of the numbers from 1 to 2512 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)

2512 / 1 = 2512 (the remainder is 0, so 1 is a divisor of 2512)
2512 / 2 = 1256 (the remainder is 0, so 2 is a divisor of 2512)
2512 / 3 = 837.33333333333 (the remainder is 1, so 3 is not a divisor of 2512)
...
2512 / 2511 = 1.0003982477101 (the remainder is 1, so 2511 is not a divisor of 2512)
2512 / 2512 = 1 (the remainder is 0, so 2512 is a divisor of 2512)

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 2512 (i.e. 50.119856344567). 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 $\frac{N}{d} = D$ )

2512 / 1 = 2512 (the remainder is 0, so 1 and 2512 are divisors of 2512)
2512 / 2 = 1256 (the remainder is 0, so 2 and 1256 are divisors of 2512)
2512 / 3 = 837.33333333333 (the remainder is 1, so 3 is not a divisor of 2512)
...
2512 / 49 = 51.265306122449 (the remainder is 13, so 49 is not a divisor of 2512)
2512 / 50 = 50.24 (the remainder is 12, so 50 is not a divisor of 2512)