What are the divisors of 4433?

1, 11, 13, 31, 143, 341, 403, 4433

There is a total of 8 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 672.

8 odd divisors

1, 11, 13, 31, 143, 341, 403, 4433

How to compute the divisors of 4433?

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 4433 by each of the numbers from 1 to 4433 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)

4433 / 1 = 4433 (the remainder is 0, so 1 is a divisor of 4433)
4433 / 2 = 2216.5 (the remainder is 1, so 2 is not a divisor of 4433)
4433 / 3 = 1477.6666666667 (the remainder is 2, so 3 is not a divisor of 4433)
...
4433 / 4432 = 1.000225631769 (the remainder is 1, so 4432 is not a divisor of 4433)
4433 / 4433 = 1 (the remainder is 0, so 4433 is a divisor of 4433)

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 4433 (i.e. 66.580778006869). 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 $\frac{N}{d} = D$ )

4433 / 1 = 4433 (the remainder is 0, so 1 and 4433 are divisors of 4433)
4433 / 2 = 2216.5 (the remainder is 1, so 2 is not a divisor of 4433)
4433 / 3 = 1477.6666666667 (the remainder is 2, so 3 is not a divisor of 4433)
...
4433 / 65 = 68.2 (the remainder is 13, so 65 is not a divisor of 4433)
4433 / 66 = 67.166666666667 (the remainder is 11, so 66 is not a divisor of 4433)