What are the divisors of 4385?

1, 5, 877, 4385

There is a total of 4 positive divisors.
The sum of these divisors is 5268.
The arithmetic mean is 1317.

4 odd divisors

1, 5, 877, 4385

How to compute the divisors of 4385?

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 4385 by each of the numbers from 1 to 4385 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)

4385 / 1 = 4385 (the remainder is 0, so 1 is a divisor of 4385)
4385 / 2 = 2192.5 (the remainder is 1, so 2 is not a divisor of 4385)
4385 / 3 = 1461.6666666667 (the remainder is 2, so 3 is not a divisor of 4385)
...
4385 / 4384 = 1.0002281021898 (the remainder is 1, so 4384 is not a divisor of 4385)
4385 / 4385 = 1 (the remainder is 0, so 4385 is a divisor of 4385)

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 4385 (i.e. 66.219332524573). 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 $\frac{N}{d} = D$ )

4385 / 1 = 4385 (the remainder is 0, so 1 and 4385 are divisors of 4385)
4385 / 2 = 2192.5 (the remainder is 1, so 2 is not a divisor of 4385)
4385 / 3 = 1461.6666666667 (the remainder is 2, so 3 is not a divisor of 4385)
...
4385 / 65 = 67.461538461538 (the remainder is 30, so 65 is not a divisor of 4385)
4385 / 66 = 66.439393939394 (the remainder is 29, so 66 is not a divisor of 4385)