What are the divisors of 489?

1, 3, 163, 489

There is a total of 4 positive divisors.
The sum of these divisors is 656.
The arithmetic mean is 164.

4 odd divisors

1, 3, 163, 489

How to compute the divisors of 489?

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 489 by each of the numbers from 1 to 489 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)

489 / 1 = 489 (the remainder is 0, so 1 is a divisor of 489)
489 / 2 = 244.5 (the remainder is 1, so 2 is not a divisor of 489)
489 / 3 = 163 (the remainder is 0, so 3 is a divisor of 489)
...
489 / 488 = 1.0020491803279 (the remainder is 1, so 488 is not a divisor of 489)
489 / 489 = 1 (the remainder is 0, so 489 is a divisor of 489)

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 489 (i.e. 22.113344387496). 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 $\frac{N}{d} = D$ )

489 / 1 = 489 (the remainder is 0, so 1 and 489 are divisors of 489)
489 / 2 = 244.5 (the remainder is 1, so 2 is not a divisor of 489)
489 / 3 = 163 (the remainder is 0, so 3 and 163 are divisors of 489)
...
489 / 21 = 23.285714285714 (the remainder is 6, so 21 is not a divisor of 489)
489 / 22 = 22.227272727273 (the remainder is 5, so 22 is not a divisor of 489)