What are the divisors of 5021?

1, 5021

There is a total of 2 positive divisors.
The sum of these divisors is 5022.
The arithmetic mean is 2511.

2 odd divisors

1, 5021

How to compute the divisors of 5021?

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 5021 by each of the numbers from 1 to 5021 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)

5021 / 1 = 5021 (the remainder is 0, so 1 is a divisor of 5021)
5021 / 2 = 2510.5 (the remainder is 1, so 2 is not a divisor of 5021)
5021 / 3 = 1673.6666666667 (the remainder is 2, so 3 is not a divisor of 5021)
...
5021 / 5020 = 1.0001992031873 (the remainder is 1, so 5020 is not a divisor of 5021)
5021 / 5021 = 1 (the remainder is 0, so 5021 is a divisor of 5021)

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 5021 (i.e. 70.859014952227). 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 $\frac{N}{d} = D$ )

5021 / 1 = 5021 (the remainder is 0, so 1 and 5021 are divisors of 5021)
5021 / 2 = 2510.5 (the remainder is 1, so 2 is not a divisor of 5021)
5021 / 3 = 1673.6666666667 (the remainder is 2, so 3 is not a divisor of 5021)
...
5021 / 69 = 72.768115942029 (the remainder is 53, so 69 is not a divisor of 5021)
5021 / 70 = 71.728571428571 (the remainder is 51, so 70 is not a divisor of 5021)