What are the divisors of 4330?

1, 2, 5, 10, 433, 866, 2165, 4330

There is a total of 8 positive divisors.
The sum of these divisors is 7812.
The arithmetic mean is 976.5.

4 even divisors

2, 10, 866, 4330

4 odd divisors

1, 5, 433, 2165

How to compute the divisors of 4330?

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 4330 by each of the numbers from 1 to 4330 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)

4330 / 1 = 4330 (the remainder is 0, so 1 is a divisor of 4330)
4330 / 2 = 2165 (the remainder is 0, so 2 is a divisor of 4330)
4330 / 3 = 1443.3333333333 (the remainder is 1, so 3 is not a divisor of 4330)
...
4330 / 4329 = 1.000231000231 (the remainder is 1, so 4329 is not a divisor of 4330)
4330 / 4330 = 1 (the remainder is 0, so 4330 is a divisor of 4330)

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 4330 (i.e. 65.802735505448). 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 $\frac{N}{d} = D$ )

4330 / 1 = 4330 (the remainder is 0, so 1 and 4330 are divisors of 4330)
4330 / 2 = 2165 (the remainder is 0, so 2 and 2165 are divisors of 4330)
4330 / 3 = 1443.3333333333 (the remainder is 1, so 3 is not a divisor of 4330)
...
4330 / 64 = 67.65625 (the remainder is 42, so 64 is not a divisor of 4330)
4330 / 65 = 66.615384615385 (the remainder is 40, so 65 is not a divisor of 4330)