What are the divisors of 5039?

1, 5039

There is a total of 2 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 2520.

2 odd divisors

1, 5039

How to compute the divisors of 5039?

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 5039 by each of the numbers from 1 to 5039 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)

5039 / 1 = 5039 (the remainder is 0, so 1 is a divisor of 5039)
5039 / 2 = 2519.5 (the remainder is 1, so 2 is not a divisor of 5039)
5039 / 3 = 1679.6666666667 (the remainder is 2, so 3 is not a divisor of 5039)
...
5039 / 5038 = 1.0001984914649 (the remainder is 1, so 5038 is not a divisor of 5039)
5039 / 5039 = 1 (the remainder is 0, so 5039 is a divisor of 5039)

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 5039 (i.e. 70.985914095685). 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 $\frac{N}{d} = D$ )

5039 / 1 = 5039 (the remainder is 0, so 1 and 5039 are divisors of 5039)
5039 / 2 = 2519.5 (the remainder is 1, so 2 is not a divisor of 5039)
5039 / 3 = 1679.6666666667 (the remainder is 2, so 3 is not a divisor of 5039)
...
5039 / 69 = 73.028985507246 (the remainder is 2, so 69 is not a divisor of 5039)
5039 / 70 = 71.985714285714 (the remainder is 69, so 70 is not a divisor of 5039)