What are the divisors of 1443?

1, 3, 13, 37, 39, 111, 481, 1443

There is a total of 8 positive divisors.
The sum of these divisors is 2128.
The arithmetic mean is 266.

8 odd divisors

1, 3, 13, 37, 39, 111, 481, 1443

How to compute the divisors of 1443?

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 1443 by each of the numbers from 1 to 1443 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)

1443 / 1 = 1443 (the remainder is 0, so 1 is a divisor of 1443)
1443 / 2 = 721.5 (the remainder is 1, so 2 is not a divisor of 1443)
1443 / 3 = 481 (the remainder is 0, so 3 is a divisor of 1443)
...
1443 / 1442 = 1.000693481276 (the remainder is 1, so 1442 is not a divisor of 1443)
1443 / 1443 = 1 (the remainder is 0, so 1443 is a divisor of 1443)

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 1443 (i.e. 37.986839826445). 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 $\frac{N}{d} = D$ )

1443 / 1 = 1443 (the remainder is 0, so 1 and 1443 are divisors of 1443)
1443 / 2 = 721.5 (the remainder is 1, so 2 is not a divisor of 1443)
1443 / 3 = 481 (the remainder is 0, so 3 and 481 are divisors of 1443)
...
1443 / 36 = 40.083333333333 (the remainder is 3, so 36 is not a divisor of 1443)
1443 / 37 = 39 (the remainder is 0, so 37 and 39 are divisors of 1443)