What are the divisors of 5073?

1, 3, 19, 57, 89, 267, 1691, 5073

There is a total of 8 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 900.

8 odd divisors

1, 3, 19, 57, 89, 267, 1691, 5073

How to compute the divisors of 5073?

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 5073 by each of the numbers from 1 to 5073 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)

5073 / 1 = 5073 (the remainder is 0, so 1 is a divisor of 5073)
5073 / 2 = 2536.5 (the remainder is 1, so 2 is not a divisor of 5073)
5073 / 3 = 1691 (the remainder is 0, so 3 is a divisor of 5073)
...
5073 / 5072 = 1.0001971608833 (the remainder is 1, so 5072 is not a divisor of 5073)
5073 / 5073 = 1 (the remainder is 0, so 5073 is a divisor of 5073)

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 5073 (i.e. 71.224995612495). 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 $\frac{N}{d} = D$ )

5073 / 1 = 5073 (the remainder is 0, so 1 and 5073 are divisors of 5073)
5073 / 2 = 2536.5 (the remainder is 1, so 2 is not a divisor of 5073)
5073 / 3 = 1691 (the remainder is 0, so 3 and 1691 are divisors of 5073)
...
5073 / 70 = 72.471428571429 (the remainder is 33, so 70 is not a divisor of 5073)
5073 / 71 = 71.450704225352 (the remainder is 32, so 71 is not a divisor of 5073)