What are the divisors of 483?

1, 3, 7, 21, 23, 69, 161, 483

There is a total of 8 positive divisors.
The sum of these divisors is 768.
The arithmetic mean is 96.

8 odd divisors

1, 3, 7, 21, 23, 69, 161, 483

How to compute the divisors of 483?

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 483 by each of the numbers from 1 to 483 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)

483 / 1 = 483 (the remainder is 0, so 1 is a divisor of 483)
483 / 2 = 241.5 (the remainder is 1, so 2 is not a divisor of 483)
483 / 3 = 161 (the remainder is 0, so 3 is a divisor of 483)
...
483 / 482 = 1.0020746887967 (the remainder is 1, so 482 is not a divisor of 483)
483 / 483 = 1 (the remainder is 0, so 483 is a divisor of 483)

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 483 (i.e. 21.977260975836). 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 $\frac{N}{d} = D$ )

483 / 1 = 483 (the remainder is 0, so 1 and 483 are divisors of 483)
483 / 2 = 241.5 (the remainder is 1, so 2 is not a divisor of 483)
483 / 3 = 161 (the remainder is 0, so 3 and 161 are divisors of 483)
...
483 / 20 = 24.15 (the remainder is 3, so 20 is not a divisor of 483)
483 / 21 = 23 (the remainder is 0, so 21 and 23 are divisors of 483)