What are the divisors of 5016?

1, 2, 3, 4, 6, 8, 11, 12, 19, 22, 24, 33, 38, 44, 57, 66, 76, 88, 114, 132, 152, 209, 228, 264, 418, 456, 627, 836, 1254, 1672, 2508, 5016

There is a total of 32 positive divisors.
The sum of these divisors is 14400.
The arithmetic mean is 450.

24 even divisors

2, 4, 6, 8, 12, 22, 24, 38, 44, 66, 76, 88, 114, 132, 152, 228, 264, 418, 456, 836, 1254, 1672, 2508, 5016

8 odd divisors

1, 3, 11, 19, 33, 57, 209, 627

How to compute the divisors of 5016?

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 5016 by each of the numbers from 1 to 5016 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)

5016 / 1 = 5016 (the remainder is 0, so 1 is a divisor of 5016)
5016 / 2 = 2508 (the remainder is 0, so 2 is a divisor of 5016)
5016 / 3 = 1672 (the remainder is 0, so 3 is a divisor of 5016)
...
5016 / 5015 = 1.0001994017946 (the remainder is 1, so 5015 is not a divisor of 5016)
5016 / 5016 = 1 (the remainder is 0, so 5016 is a divisor of 5016)

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 5016 (i.e. 70.823724838503). 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 $\frac{N}{d} = D$ )

5016 / 1 = 5016 (the remainder is 0, so 1 and 5016 are divisors of 5016)
5016 / 2 = 2508 (the remainder is 0, so 2 and 2508 are divisors of 5016)
5016 / 3 = 1672 (the remainder is 0, so 3 and 1672 are divisors of 5016)
...
5016 / 69 = 72.695652173913 (the remainder is 48, so 69 is not a divisor of 5016)
5016 / 70 = 71.657142857143 (the remainder is 46, so 70 is not a divisor of 5016)