What are the divisors of 447?

1, 3, 149, 447

There is a total of 4 positive divisors.
The sum of these divisors is 600.
The arithmetic mean is 150.

4 odd divisors

1, 3, 149, 447

How to compute the divisors of 447?

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 447 by each of the numbers from 1 to 447 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)

447 / 1 = 447 (the remainder is 0, so 1 is a divisor of 447)
447 / 2 = 223.5 (the remainder is 1, so 2 is not a divisor of 447)
447 / 3 = 149 (the remainder is 0, so 3 is a divisor of 447)
...
447 / 446 = 1.0022421524664 (the remainder is 1, so 446 is not a divisor of 447)
447 / 447 = 1 (the remainder is 0, so 447 is a divisor of 447)

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 447 (i.e. 21.142374511866). 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 $\frac{N}{d} = D$ )

447 / 1 = 447 (the remainder is 0, so 1 and 447 are divisors of 447)
447 / 2 = 223.5 (the remainder is 1, so 2 is not a divisor of 447)
447 / 3 = 149 (the remainder is 0, so 3 and 149 are divisors of 447)
...
447 / 20 = 22.35 (the remainder is 7, so 20 is not a divisor of 447)
447 / 21 = 21.285714285714 (the remainder is 6, so 21 is not a divisor of 447)