What are the divisors of 5045?

1, 5, 1009, 5045

There is a total of 4 positive divisors.
The sum of these divisors is 6060.
The arithmetic mean is 1515.

4 odd divisors

1, 5, 1009, 5045

How to compute the divisors of 5045?

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 5045 by each of the numbers from 1 to 5045 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)

5045 / 1 = 5045 (the remainder is 0, so 1 is a divisor of 5045)
5045 / 2 = 2522.5 (the remainder is 1, so 2 is not a divisor of 5045)
5045 / 3 = 1681.6666666667 (the remainder is 2, so 3 is not a divisor of 5045)
...
5045 / 5044 = 1.0001982553529 (the remainder is 1, so 5044 is not a divisor of 5045)
5045 / 5045 = 1 (the remainder is 0, so 5045 is a divisor of 5045)

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 5045 (i.e. 71.028163428319). 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 $\frac{N}{d} = D$ )

5045 / 1 = 5045 (the remainder is 0, so 1 and 5045 are divisors of 5045)
5045 / 2 = 2522.5 (the remainder is 1, so 2 is not a divisor of 5045)
5045 / 3 = 1681.6666666667 (the remainder is 2, so 3 is not a divisor of 5045)
...
5045 / 70 = 72.071428571429 (the remainder is 5, so 70 is not a divisor of 5045)
5045 / 71 = 71.056338028169 (the remainder is 4, so 71 is not a divisor of 5045)