What are the divisors of 4405?

1, 5, 881, 4405

There is a total of 4 positive divisors.
The sum of these divisors is 5292.
The arithmetic mean is 1323.

4 odd divisors

1, 5, 881, 4405

How to compute the divisors of 4405?

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 4405 by each of the numbers from 1 to 4405 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)

4405 / 1 = 4405 (the remainder is 0, so 1 is a divisor of 4405)
4405 / 2 = 2202.5 (the remainder is 1, so 2 is not a divisor of 4405)
4405 / 3 = 1468.3333333333 (the remainder is 1, so 3 is not a divisor of 4405)
...
4405 / 4404 = 1.0002270663034 (the remainder is 1, so 4404 is not a divisor of 4405)
4405 / 4405 = 1 (the remainder is 0, so 4405 is a divisor of 4405)

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 4405 (i.e. 66.37017402418). 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 $\frac{N}{d} = D$ )

4405 / 1 = 4405 (the remainder is 0, so 1 and 4405 are divisors of 4405)
4405 / 2 = 2202.5 (the remainder is 1, so 2 is not a divisor of 4405)
4405 / 3 = 1468.3333333333 (the remainder is 1, so 3 is not a divisor of 4405)
...
4405 / 65 = 67.769230769231 (the remainder is 50, so 65 is not a divisor of 4405)
4405 / 66 = 66.742424242424 (the remainder is 49, so 66 is not a divisor of 4405)