What are the divisors of 5069?

1, 37, 137, 5069

There is a total of 4 positive divisors.
The sum of these divisors is 5244.
The arithmetic mean is 1311.

4 odd divisors

1, 37, 137, 5069

How to compute the divisors of 5069?

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 5069 by each of the numbers from 1 to 5069 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)

5069 / 1 = 5069 (the remainder is 0, so 1 is a divisor of 5069)
5069 / 2 = 2534.5 (the remainder is 1, so 2 is not a divisor of 5069)
5069 / 3 = 1689.6666666667 (the remainder is 2, so 3 is not a divisor of 5069)
...
5069 / 5068 = 1.0001973164957 (the remainder is 1, so 5068 is not a divisor of 5069)
5069 / 5069 = 1 (the remainder is 0, so 5069 is a divisor of 5069)

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 5069 (i.e. 71.19691004531). 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 $\frac{N}{d} = D$ )

5069 / 1 = 5069 (the remainder is 0, so 1 and 5069 are divisors of 5069)
5069 / 2 = 2534.5 (the remainder is 1, so 2 is not a divisor of 5069)
5069 / 3 = 1689.6666666667 (the remainder is 2, so 3 is not a divisor of 5069)
...
5069 / 70 = 72.414285714286 (the remainder is 29, so 70 is not a divisor of 5069)
5069 / 71 = 71.394366197183 (the remainder is 28, so 71 is not a divisor of 5069)