What are the divisors of 4358?

1, 2, 2179, 4358

There is a total of 4 positive divisors.
The sum of these divisors is 6540.
The arithmetic mean is 1635.

2 even divisors

2, 4358

2 odd divisors

1, 2179

How to compute the divisors of 4358?

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 4358 by each of the numbers from 1 to 4358 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)

4358 / 1 = 4358 (the remainder is 0, so 1 is a divisor of 4358)
4358 / 2 = 2179 (the remainder is 0, so 2 is a divisor of 4358)
4358 / 3 = 1452.6666666667 (the remainder is 2, so 3 is not a divisor of 4358)
...
4358 / 4357 = 1.0002295157218 (the remainder is 1, so 4357 is not a divisor of 4358)
4358 / 4358 = 1 (the remainder is 0, so 4358 is a divisor of 4358)

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 4358 (i.e. 66.015149776396). 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 $\frac{N}{d} = D$ )

4358 / 1 = 4358 (the remainder is 0, so 1 and 4358 are divisors of 4358)
4358 / 2 = 2179 (the remainder is 0, so 2 and 2179 are divisors of 4358)
4358 / 3 = 1452.6666666667 (the remainder is 2, so 3 is not a divisor of 4358)
...
4358 / 65 = 67.046153846154 (the remainder is 3, so 65 is not a divisor of 4358)
4358 / 66 = 66.030303030303 (the remainder is 2, so 66 is not a divisor of 4358)