What are the divisors of 4359?

1, 3, 1453, 4359

There is a total of 4 positive divisors.
The sum of these divisors is 5816.
The arithmetic mean is 1454.

4 odd divisors

1, 3, 1453, 4359

How to compute the divisors of 4359?

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 4359 by each of the numbers from 1 to 4359 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)

4359 / 1 = 4359 (the remainder is 0, so 1 is a divisor of 4359)
4359 / 2 = 2179.5 (the remainder is 1, so 2 is not a divisor of 4359)
4359 / 3 = 1453 (the remainder is 0, so 3 is a divisor of 4359)
...
4359 / 4358 = 1.0002294630564 (the remainder is 1, so 4358 is not a divisor of 4359)
4359 / 4359 = 1 (the remainder is 0, so 4359 is a divisor of 4359)

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 4359 (i.e. 66.022723360976). 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 $\frac{N}{d} = D$ )

4359 / 1 = 4359 (the remainder is 0, so 1 and 4359 are divisors of 4359)
4359 / 2 = 2179.5 (the remainder is 1, so 2 is not a divisor of 4359)
4359 / 3 = 1453 (the remainder is 0, so 3 and 1453 are divisors of 4359)
...
4359 / 65 = 67.061538461538 (the remainder is 4, so 65 is not a divisor of 4359)
4359 / 66 = 66.045454545455 (the remainder is 3, so 66 is not a divisor of 4359)