What are the divisors of 4859?

1, 43, 113, 4859

There is a total of 4 positive divisors.
The sum of these divisors is 5016.
The arithmetic mean is 1254.

4 odd divisors

1, 43, 113, 4859

How to compute the divisors of 4859?

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 4859 by each of the numbers from 1 to 4859 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)

4859 / 1 = 4859 (the remainder is 0, so 1 is a divisor of 4859)
4859 / 2 = 2429.5 (the remainder is 1, so 2 is not a divisor of 4859)
4859 / 3 = 1619.6666666667 (the remainder is 2, so 3 is not a divisor of 4859)
...
4859 / 4858 = 1.0002058460272 (the remainder is 1, so 4858 is not a divisor of 4859)
4859 / 4859 = 1 (the remainder is 0, so 4859 is a divisor of 4859)

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 4859 (i.e. 69.706527671374). 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 $\frac{N}{d} = D$ )

4859 / 1 = 4859 (the remainder is 0, so 1 and 4859 are divisors of 4859)
4859 / 2 = 2429.5 (the remainder is 1, so 2 is not a divisor of 4859)
4859 / 3 = 1619.6666666667 (the remainder is 2, so 3 is not a divisor of 4859)
...
4859 / 68 = 71.455882352941 (the remainder is 31, so 68 is not a divisor of 4859)
4859 / 69 = 70.420289855072 (the remainder is 29, so 69 is not a divisor of 4859)