What are the divisors of 4887?

1, 3, 9, 27, 181, 543, 1629, 4887

There is a total of 8 positive divisors.
The sum of these divisors is 7280.
The arithmetic mean is 910.

8 odd divisors

1, 3, 9, 27, 181, 543, 1629, 4887

How to compute the divisors of 4887?

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 4887 by each of the numbers from 1 to 4887 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)

4887 / 1 = 4887 (the remainder is 0, so 1 is a divisor of 4887)
4887 / 2 = 2443.5 (the remainder is 1, so 2 is not a divisor of 4887)
4887 / 3 = 1629 (the remainder is 0, so 3 is a divisor of 4887)
...
4887 / 4886 = 1.0002046663938 (the remainder is 1, so 4886 is not a divisor of 4887)
4887 / 4887 = 1 (the remainder is 0, so 4887 is a divisor of 4887)

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 4887 (i.e. 69.907081186386). 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 $\frac{N}{d} = D$ )

4887 / 1 = 4887 (the remainder is 0, so 1 and 4887 are divisors of 4887)
4887 / 2 = 2443.5 (the remainder is 1, so 2 is not a divisor of 4887)
4887 / 3 = 1629 (the remainder is 0, so 3 and 1629 are divisors of 4887)
...
4887 / 68 = 71.867647058824 (the remainder is 59, so 68 is not a divisor of 4887)
4887 / 69 = 70.826086956522 (the remainder is 57, so 69 is not a divisor of 4887)