What are the divisors of 5186?

1, 2, 2593, 5186

There is a total of 4 positive divisors.
The sum of these divisors is 7782.
The arithmetic mean is 1945.5.

2 even divisors

2, 5186

2 odd divisors

1, 2593

How to compute the divisors of 5186?

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 5186 by each of the numbers from 1 to 5186 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)

5186 / 1 = 5186 (the remainder is 0, so 1 is a divisor of 5186)
5186 / 2 = 2593 (the remainder is 0, so 2 is a divisor of 5186)
5186 / 3 = 1728.6666666667 (the remainder is 2, so 3 is not a divisor of 5186)
...
5186 / 5185 = 1.0001928640309 (the remainder is 1, so 5185 is not a divisor of 5186)
5186 / 5186 = 1 (the remainder is 0, so 5186 is a divisor of 5186)

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 5186 (i.e. 72.013887549555). 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 $\frac{N}{d} = D$ )

5186 / 1 = 5186 (the remainder is 0, so 1 and 5186 are divisors of 5186)
5186 / 2 = 2593 (the remainder is 0, so 2 and 2593 are divisors of 5186)
5186 / 3 = 1728.6666666667 (the remainder is 2, so 3 is not a divisor of 5186)
...
5186 / 71 = 73.042253521127 (the remainder is 3, so 71 is not a divisor of 5186)
5186 / 72 = 72.027777777778 (the remainder is 2, so 72 is not a divisor of 5186)