What are the divisors of 4409?

1, 4409

There is a total of 2 positive divisors.
The sum of these divisors is 4410.
The arithmetic mean is 2205.

2 odd divisors

1, 4409

How to compute the divisors of 4409?

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 4409 by each of the numbers from 1 to 4409 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)

4409 / 1 = 4409 (the remainder is 0, so 1 is a divisor of 4409)
4409 / 2 = 2204.5 (the remainder is 1, so 2 is not a divisor of 4409)
4409 / 3 = 1469.6666666667 (the remainder is 2, so 3 is not a divisor of 4409)
...
4409 / 4408 = 1.0002268602541 (the remainder is 1, so 4408 is not a divisor of 4409)
4409 / 4409 = 1 (the remainder is 0, so 4409 is a divisor of 4409)

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 4409 (i.e. 66.400301204136). 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 $\frac{N}{d} = D$ )

4409 / 1 = 4409 (the remainder is 0, so 1 and 4409 are divisors of 4409)
4409 / 2 = 2204.5 (the remainder is 1, so 2 is not a divisor of 4409)
4409 / 3 = 1469.6666666667 (the remainder is 2, so 3 is not a divisor of 4409)
...
4409 / 65 = 67.830769230769 (the remainder is 54, so 65 is not a divisor of 4409)
4409 / 66 = 66.80303030303 (the remainder is 53, so 66 is not a divisor of 4409)