What are the divisors of 5065?

1, 5, 1013, 5065

There is a total of 4 positive divisors.
The sum of these divisors is 6084.
The arithmetic mean is 1521.

4 odd divisors

1, 5, 1013, 5065

How to compute the divisors of 5065?

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 5065 by each of the numbers from 1 to 5065 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)

5065 / 1 = 5065 (the remainder is 0, so 1 is a divisor of 5065)
5065 / 2 = 2532.5 (the remainder is 1, so 2 is not a divisor of 5065)
5065 / 3 = 1688.3333333333 (the remainder is 1, so 3 is not a divisor of 5065)
...
5065 / 5064 = 1.0001974723539 (the remainder is 1, so 5064 is not a divisor of 5065)
5065 / 5065 = 1 (the remainder is 0, so 5065 is a divisor of 5065)

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 5065 (i.e. 71.168813394632). 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 $\frac{N}{d} = D$ )

5065 / 1 = 5065 (the remainder is 0, so 1 and 5065 are divisors of 5065)
5065 / 2 = 2532.5 (the remainder is 1, so 2 is not a divisor of 5065)
5065 / 3 = 1688.3333333333 (the remainder is 1, so 3 is not a divisor of 5065)
...
5065 / 70 = 72.357142857143 (the remainder is 25, so 70 is not a divisor of 5065)
5065 / 71 = 71.338028169014 (the remainder is 24, so 71 is not a divisor of 5065)