What are the divisors of 4350?

1, 2, 3, 5, 6, 10, 15, 25, 29, 30, 50, 58, 75, 87, 145, 150, 174, 290, 435, 725, 870, 1450, 2175, 4350

There is a total of 24 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 465.

12 even divisors

2, 6, 10, 30, 50, 58, 150, 174, 290, 870, 1450, 4350

12 odd divisors

1, 3, 5, 15, 25, 29, 75, 87, 145, 435, 725, 2175

How to compute the divisors of 4350?

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 4350 by each of the numbers from 1 to 4350 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)

4350 / 1 = 4350 (the remainder is 0, so 1 is a divisor of 4350)
4350 / 2 = 2175 (the remainder is 0, so 2 is a divisor of 4350)
4350 / 3 = 1450 (the remainder is 0, so 3 is a divisor of 4350)
...
4350 / 4349 = 1.0002299379168 (the remainder is 1, so 4349 is not a divisor of 4350)
4350 / 4350 = 1 (the remainder is 0, so 4350 is a divisor of 4350)

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 4350 (i.e. 65.954529791365). 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 $\frac{N}{d} = D$ )

4350 / 1 = 4350 (the remainder is 0, so 1 and 4350 are divisors of 4350)
4350 / 2 = 2175 (the remainder is 0, so 2 and 2175 are divisors of 4350)
4350 / 3 = 1450 (the remainder is 0, so 3 and 1450 are divisors of 4350)
...
4350 / 64 = 67.96875 (the remainder is 62, so 64 is not a divisor of 4350)
4350 / 65 = 66.923076923077 (the remainder is 60, so 65 is not a divisor of 4350)