What are the divisors of 4430?

1, 2, 5, 10, 443, 886, 2215, 4430

There is a total of 8 positive divisors.
The sum of these divisors is 7992.
The arithmetic mean is 999.

4 even divisors

2, 10, 886, 4430

4 odd divisors

1, 5, 443, 2215

How to compute the divisors of 4430?

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 4430 by each of the numbers from 1 to 4430 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)

4430 / 1 = 4430 (the remainder is 0, so 1 is a divisor of 4430)
4430 / 2 = 2215 (the remainder is 0, so 2 is a divisor of 4430)
4430 / 3 = 1476.6666666667 (the remainder is 2, so 3 is not a divisor of 4430)
...
4430 / 4429 = 1.0002257846015 (the remainder is 1, so 4429 is not a divisor of 4430)
4430 / 4430 = 1 (the remainder is 0, so 4430 is a divisor of 4430)

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 4430 (i.e. 66.558245169175). 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 $\frac{N}{d} = D$ )

4430 / 1 = 4430 (the remainder is 0, so 1 and 4430 are divisors of 4430)
4430 / 2 = 2215 (the remainder is 0, so 2 and 2215 are divisors of 4430)
4430 / 3 = 1476.6666666667 (the remainder is 2, so 3 is not a divisor of 4430)
...
4430 / 65 = 68.153846153846 (the remainder is 10, so 65 is not a divisor of 4430)
4430 / 66 = 67.121212121212 (the remainder is 8, so 66 is not a divisor of 4430)