What are the divisors of 4873?

1, 11, 443, 4873

There is a total of 4 positive divisors.
The sum of these divisors is 5328.
The arithmetic mean is 1332.

4 odd divisors

1, 11, 443, 4873

How to compute the divisors of 4873?

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 4873 by each of the numbers from 1 to 4873 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)

4873 / 1 = 4873 (the remainder is 0, so 1 is a divisor of 4873)
4873 / 2 = 2436.5 (the remainder is 1, so 2 is not a divisor of 4873)
4873 / 3 = 1624.3333333333 (the remainder is 1, so 3 is not a divisor of 4873)
...
4873 / 4872 = 1.0002052545156 (the remainder is 1, so 4872 is not a divisor of 4873)
4873 / 4873 = 1 (the remainder is 0, so 4873 is a divisor of 4873)

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 4873 (i.e. 69.806876452109). 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 $\frac{N}{d} = D$ )

4873 / 1 = 4873 (the remainder is 0, so 1 and 4873 are divisors of 4873)
4873 / 2 = 2436.5 (the remainder is 1, so 2 is not a divisor of 4873)
4873 / 3 = 1624.3333333333 (the remainder is 1, so 3 is not a divisor of 4873)
...
4873 / 68 = 71.661764705882 (the remainder is 45, so 68 is not a divisor of 4873)
4873 / 69 = 70.623188405797 (the remainder is 43, so 69 is not a divisor of 4873)