What are the divisors of 5012?

1, 2, 4, 7, 14, 28, 179, 358, 716, 1253, 2506, 5012

There is a total of 12 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 840.

8 even divisors

2, 4, 14, 28, 358, 716, 2506, 5012

4 odd divisors

1, 7, 179, 1253

How to compute the divisors of 5012?

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 5012 by each of the numbers from 1 to 5012 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)

5012 / 1 = 5012 (the remainder is 0, so 1 is a divisor of 5012)
5012 / 2 = 2506 (the remainder is 0, so 2 is a divisor of 5012)
5012 / 3 = 1670.6666666667 (the remainder is 2, so 3 is not a divisor of 5012)
...
5012 / 5011 = 1.0001995609659 (the remainder is 1, so 5011 is not a divisor of 5012)
5012 / 5012 = 1 (the remainder is 0, so 5012 is a divisor of 5012)

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 5012 (i.e. 70.795480081711). 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 $\frac{N}{d} = D$ )

5012 / 1 = 5012 (the remainder is 0, so 1 and 5012 are divisors of 5012)
5012 / 2 = 2506 (the remainder is 0, so 2 and 2506 are divisors of 5012)
5012 / 3 = 1670.6666666667 (the remainder is 2, so 3 is not a divisor of 5012)
...
5012 / 69 = 72.63768115942 (the remainder is 44, so 69 is not a divisor of 5012)
5012 / 70 = 71.6 (the remainder is 42, so 70 is not a divisor of 5012)