What are the divisors of 5182?

1, 2, 2591, 5182

There is a total of 4 positive divisors.
The sum of these divisors is 7776.
The arithmetic mean is 1944.

2 even divisors

2, 5182

2 odd divisors

1, 2591

How to compute the divisors of 5182?

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 5182 by each of the numbers from 1 to 5182 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)

5182 / 1 = 5182 (the remainder is 0, so 1 is a divisor of 5182)
5182 / 2 = 2591 (the remainder is 0, so 2 is a divisor of 5182)
5182 / 3 = 1727.3333333333 (the remainder is 1, so 3 is not a divisor of 5182)
...
5182 / 5181 = 1.0001930129319 (the remainder is 1, so 5181 is not a divisor of 5182)
5182 / 5182 = 1 (the remainder is 0, so 5182 is a divisor of 5182)

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 5182 (i.e. 71.986109771261). 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 $\frac{N}{d} = D$ )

5182 / 1 = 5182 (the remainder is 0, so 1 and 5182 are divisors of 5182)
5182 / 2 = 2591 (the remainder is 0, so 2 and 2591 are divisors of 5182)
5182 / 3 = 1727.3333333333 (the remainder is 1, so 3 is not a divisor of 5182)
...
5182 / 70 = 74.028571428571 (the remainder is 2, so 70 is not a divisor of 5182)
5182 / 71 = 72.985915492958 (the remainder is 70, so 71 is not a divisor of 5182)