What are the divisors of 443?

1, 443

There is a total of 2 positive divisors.
The sum of these divisors is 444.
The arithmetic mean is 222.

2 odd divisors

1, 443

How to compute the divisors of 443?

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 443 by each of the numbers from 1 to 443 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)

443 / 1 = 443 (the remainder is 0, so 1 is a divisor of 443)
443 / 2 = 221.5 (the remainder is 1, so 2 is not a divisor of 443)
443 / 3 = 147.66666666667 (the remainder is 2, so 3 is not a divisor of 443)
...
443 / 442 = 1.0022624434389 (the remainder is 1, so 442 is not a divisor of 443)
443 / 443 = 1 (the remainder is 0, so 443 is a divisor of 443)

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 443 (i.e. 21.047565179849). 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 $\frac{N}{d} = D$ )

443 / 1 = 443 (the remainder is 0, so 1 and 443 are divisors of 443)
443 / 2 = 221.5 (the remainder is 1, so 2 is not a divisor of 443)
443 / 3 = 147.66666666667 (the remainder is 2, so 3 is not a divisor of 443)
...
443 / 20 = 22.15 (the remainder is 3, so 20 is not a divisor of 443)
443 / 21 = 21.095238095238 (the remainder is 2, so 21 is not a divisor of 443)