What are the divisors of 5082?

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 121, 154, 231, 242, 363, 462, 726, 847, 1694, 2541, 5082

There is a total of 24 positive divisors.
The sum of these divisors is 12768.
The arithmetic mean is 532.

12 even divisors

2, 6, 14, 22, 42, 66, 154, 242, 462, 726, 1694, 5082

12 odd divisors

1, 3, 7, 11, 21, 33, 77, 121, 231, 363, 847, 2541

How to compute the divisors of 5082?

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 5082 by each of the numbers from 1 to 5082 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)

5082 / 1 = 5082 (the remainder is 0, so 1 is a divisor of 5082)
5082 / 2 = 2541 (the remainder is 0, so 2 is a divisor of 5082)
5082 / 3 = 1694 (the remainder is 0, so 3 is a divisor of 5082)
...
5082 / 5081 = 1.0001968116512 (the remainder is 1, so 5081 is not a divisor of 5082)
5082 / 5082 = 1 (the remainder is 0, so 5082 is a divisor of 5082)

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 5082 (i.e. 71.288147682486). 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 $\frac{N}{d} = D$ )

5082 / 1 = 5082 (the remainder is 0, so 1 and 5082 are divisors of 5082)
5082 / 2 = 2541 (the remainder is 0, so 2 and 2541 are divisors of 5082)
5082 / 3 = 1694 (the remainder is 0, so 3 and 1694 are divisors of 5082)
...
5082 / 70 = 72.6 (the remainder is 42, so 70 is not a divisor of 5082)
5082 / 71 = 71.577464788732 (the remainder is 41, so 71 is not a divisor of 5082)