What are the divisors of 2516?

1, 2, 4, 17, 34, 37, 68, 74, 148, 629, 1258, 2516

There is a total of 12 positive divisors.
The sum of these divisors is 4788.
The arithmetic mean is 399.

8 even divisors

2, 4, 34, 68, 74, 148, 1258, 2516

4 odd divisors

1, 17, 37, 629

How to compute the divisors of 2516?

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 2516 by each of the numbers from 1 to 2516 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)

2516 / 1 = 2516 (the remainder is 0, so 1 is a divisor of 2516)
2516 / 2 = 1258 (the remainder is 0, so 2 is a divisor of 2516)
2516 / 3 = 838.66666666667 (the remainder is 2, so 3 is not a divisor of 2516)
...
2516 / 2515 = 1.0003976143141 (the remainder is 1, so 2515 is not a divisor of 2516)
2516 / 2516 = 1 (the remainder is 0, so 2516 is a divisor of 2516)

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 2516 (i.e. 50.159744815938). 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 $\frac{N}{d} = D$ )

2516 / 1 = 2516 (the remainder is 0, so 1 and 2516 are divisors of 2516)
2516 / 2 = 1258 (the remainder is 0, so 2 and 1258 are divisors of 2516)
2516 / 3 = 838.66666666667 (the remainder is 2, so 3 is not a divisor of 2516)
...
2516 / 49 = 51.34693877551 (the remainder is 17, so 49 is not a divisor of 2516)
2516 / 50 = 50.32 (the remainder is 16, so 50 is not a divisor of 2516)