What are the divisors of 5023?

1, 5023

There is a total of 2 positive divisors.
The sum of these divisors is 5024.
The arithmetic mean is 2512.

2 odd divisors

1, 5023

How to compute the divisors of 5023?

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 5023 by each of the numbers from 1 to 5023 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)

5023 / 1 = 5023 (the remainder is 0, so 1 is a divisor of 5023)
5023 / 2 = 2511.5 (the remainder is 1, so 2 is not a divisor of 5023)
5023 / 3 = 1674.3333333333 (the remainder is 1, so 3 is not a divisor of 5023)
...
5023 / 5022 = 1.000199123855 (the remainder is 1, so 5022 is not a divisor of 5023)
5023 / 5023 = 1 (the remainder is 0, so 5023 is a divisor of 5023)

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 5023 (i.e. 70.87312607752). 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 $\frac{N}{d} = D$ )

5023 / 1 = 5023 (the remainder is 0, so 1 and 5023 are divisors of 5023)
5023 / 2 = 2511.5 (the remainder is 1, so 2 is not a divisor of 5023)
5023 / 3 = 1674.3333333333 (the remainder is 1, so 3 is not a divisor of 5023)
...
5023 / 69 = 72.797101449275 (the remainder is 55, so 69 is not a divisor of 5023)
5023 / 70 = 71.757142857143 (the remainder is 53, so 70 is not a divisor of 5023)