What are the divisors of 4327?

1, 4327

There is a total of 2 positive divisors.
The sum of these divisors is 4328.
The arithmetic mean is 2164.

2 odd divisors

1, 4327

How to compute the divisors of 4327?

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 4327 by each of the numbers from 1 to 4327 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)

4327 / 1 = 4327 (the remainder is 0, so 1 is a divisor of 4327)
4327 / 2 = 2163.5 (the remainder is 1, so 2 is not a divisor of 4327)
4327 / 3 = 1442.3333333333 (the remainder is 1, so 3 is not a divisor of 4327)
...
4327 / 4326 = 1.0002311604253 (the remainder is 1, so 4326 is not a divisor of 4327)
4327 / 4327 = 1 (the remainder is 0, so 4327 is a divisor of 4327)

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 4327 (i.e. 65.779936150775). 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 $\frac{N}{d} = D$ )

4327 / 1 = 4327 (the remainder is 0, so 1 and 4327 are divisors of 4327)
4327 / 2 = 2163.5 (the remainder is 1, so 2 is not a divisor of 4327)
4327 / 3 = 1442.3333333333 (the remainder is 1, so 3 is not a divisor of 4327)
...
4327 / 64 = 67.609375 (the remainder is 39, so 64 is not a divisor of 4327)
4327 / 65 = 66.569230769231 (the remainder is 37, so 65 is not a divisor of 4327)