What are the divisors of 433?

1, 433

There is a total of 2 positive divisors.
The sum of these divisors is 434.
The arithmetic mean is 217.

2 odd divisors

1, 433

How to compute the divisors of 433?

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 433 by each of the numbers from 1 to 433 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)

433 / 1 = 433 (the remainder is 0, so 1 is a divisor of 433)
433 / 2 = 216.5 (the remainder is 1, so 2 is not a divisor of 433)
433 / 3 = 144.33333333333 (the remainder is 1, so 3 is not a divisor of 433)
...
433 / 432 = 1.0023148148148 (the remainder is 1, so 432 is not a divisor of 433)
433 / 433 = 1 (the remainder is 0, so 433 is a divisor of 433)

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 433 (i.e. 20.808652046685). 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 $\frac{N}{d} = D$ )

433 / 1 = 433 (the remainder is 0, so 1 and 433 are divisors of 433)
433 / 2 = 216.5 (the remainder is 1, so 2 is not a divisor of 433)
433 / 3 = 144.33333333333 (the remainder is 1, so 3 is not a divisor of 433)
...
433 / 19 = 22.789473684211 (the remainder is 15, so 19 is not a divisor of 433)
433 / 20 = 21.65 (the remainder is 13, so 20 is not a divisor of 433)