What are the divisors of 4443?

1, 3, 1481, 4443

There is a total of 4 positive divisors.
The sum of these divisors is 5928.
The arithmetic mean is 1482.

4 odd divisors

1, 3, 1481, 4443

How to compute the divisors of 4443?

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 4443 by each of the numbers from 1 to 4443 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)

4443 / 1 = 4443 (the remainder is 0, so 1 is a divisor of 4443)
4443 / 2 = 2221.5 (the remainder is 1, so 2 is not a divisor of 4443)
4443 / 3 = 1481 (the remainder is 0, so 3 is a divisor of 4443)
...
4443 / 4442 = 1.0002251238181 (the remainder is 1, so 4442 is not a divisor of 4443)
4443 / 4443 = 1 (the remainder is 0, so 4443 is a divisor of 4443)

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 4443 (i.e. 66.655832452982). 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 $\frac{N}{d} = D$ )

4443 / 1 = 4443 (the remainder is 0, so 1 and 4443 are divisors of 4443)
4443 / 2 = 2221.5 (the remainder is 1, so 2 is not a divisor of 4443)
4443 / 3 = 1481 (the remainder is 0, so 3 and 1481 are divisors of 4443)
...
4443 / 65 = 68.353846153846 (the remainder is 23, so 65 is not a divisor of 4443)
4443 / 66 = 67.318181818182 (the remainder is 21, so 66 is not a divisor of 4443)