What are the divisors of 4878?

1, 2, 3, 6, 9, 18, 271, 542, 813, 1626, 2439, 4878

There is a total of 12 positive divisors.
The sum of these divisors is 10608.
The arithmetic mean is 884.

6 even divisors

2, 6, 18, 542, 1626, 4878

6 odd divisors

1, 3, 9, 271, 813, 2439

How to compute the divisors of 4878?

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 4878 by each of the numbers from 1 to 4878 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)

4878 / 1 = 4878 (the remainder is 0, so 1 is a divisor of 4878)
4878 / 2 = 2439 (the remainder is 0, so 2 is a divisor of 4878)
4878 / 3 = 1626 (the remainder is 0, so 3 is a divisor of 4878)
...
4878 / 4877 = 1.0002050440845 (the remainder is 1, so 4877 is not a divisor of 4878)
4878 / 4878 = 1 (the remainder is 0, so 4878 is a divisor of 4878)

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 4878 (i.e. 69.842680360937). 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 $\frac{N}{d} = D$ )

4878 / 1 = 4878 (the remainder is 0, so 1 and 4878 are divisors of 4878)
4878 / 2 = 2439 (the remainder is 0, so 2 and 2439 are divisors of 4878)
4878 / 3 = 1626 (the remainder is 0, so 3 and 1626 are divisors of 4878)
...
4878 / 68 = 71.735294117647 (the remainder is 50, so 68 is not a divisor of 4878)
4878 / 69 = 70.695652173913 (the remainder is 48, so 69 is not a divisor of 4878)