What are the divisors of 4689?

1, 3, 9, 521, 1563, 4689

There is a total of 6 positive divisors.
The sum of these divisors is 6786.
The arithmetic mean is 1131.

6 odd divisors

1, 3, 9, 521, 1563, 4689

How to compute the divisors of 4689?

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 4689 by each of the numbers from 1 to 4689 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)

4689 / 1 = 4689 (the remainder is 0, so 1 is a divisor of 4689)
4689 / 2 = 2344.5 (the remainder is 1, so 2 is not a divisor of 4689)
4689 / 3 = 1563 (the remainder is 0, so 3 is a divisor of 4689)
...
4689 / 4688 = 1.0002133105802 (the remainder is 1, so 4688 is not a divisor of 4689)
4689 / 4689 = 1 (the remainder is 0, so 4689 is a divisor of 4689)

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 4689 (i.e. 68.47627326308). 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 $\frac{N}{d} = D$ )

4689 / 1 = 4689 (the remainder is 0, so 1 and 4689 are divisors of 4689)
4689 / 2 = 2344.5 (the remainder is 1, so 2 is not a divisor of 4689)
4689 / 3 = 1563 (the remainder is 0, so 3 and 1563 are divisors of 4689)
...
4689 / 67 = 69.985074626866 (the remainder is 66, so 67 is not a divisor of 4689)
4689 / 68 = 68.955882352941 (the remainder is 65, so 68 is not a divisor of 4689)