What are the divisors of 4889?

1, 4889

There is a total of 2 positive divisors.
The sum of these divisors is 4890.
The arithmetic mean is 2445.

2 odd divisors

1, 4889

How to compute the divisors of 4889?

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 4889 by each of the numbers from 1 to 4889 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)

4889 / 1 = 4889 (the remainder is 0, so 1 is a divisor of 4889)
4889 / 2 = 2444.5 (the remainder is 1, so 2 is not a divisor of 4889)
4889 / 3 = 1629.6666666667 (the remainder is 2, so 3 is not a divisor of 4889)
...
4889 / 4888 = 1.0002045826514 (the remainder is 1, so 4888 is not a divisor of 4889)
4889 / 4889 = 1 (the remainder is 0, so 4889 is a divisor of 4889)

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 4889 (i.e. 69.921384425653). 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 $\frac{N}{d} = D$ )

4889 / 1 = 4889 (the remainder is 0, so 1 and 4889 are divisors of 4889)
4889 / 2 = 2444.5 (the remainder is 1, so 2 is not a divisor of 4889)
4889 / 3 = 1629.6666666667 (the remainder is 2, so 3 is not a divisor of 4889)
...
4889 / 68 = 71.897058823529 (the remainder is 61, so 68 is not a divisor of 4889)
4889 / 69 = 70.855072463768 (the remainder is 59, so 69 is not a divisor of 4889)