What are the divisors of 4360?

1, 2, 4, 5, 8, 10, 20, 40, 109, 218, 436, 545, 872, 1090, 2180, 4360

There is a total of 16 positive divisors.
The sum of these divisors is 9900.
The arithmetic mean is 618.75.

12 even divisors

2, 4, 8, 10, 20, 40, 218, 436, 872, 1090, 2180, 4360

4 odd divisors

1, 5, 109, 545

How to compute the divisors of 4360?

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 4360 by each of the numbers from 1 to 4360 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)

4360 / 1 = 4360 (the remainder is 0, so 1 is a divisor of 4360)
4360 / 2 = 2180 (the remainder is 0, so 2 is a divisor of 4360)
4360 / 3 = 1453.3333333333 (the remainder is 1, so 3 is not a divisor of 4360)
...
4360 / 4359 = 1.0002294104152 (the remainder is 1, so 4359 is not a divisor of 4360)
4360 / 4360 = 1 (the remainder is 0, so 4360 is a divisor of 4360)

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 4360 (i.e. 66.030296076877). 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 $\frac{N}{d} = D$ )

4360 / 1 = 4360 (the remainder is 0, so 1 and 4360 are divisors of 4360)
4360 / 2 = 2180 (the remainder is 0, so 2 and 2180 are divisors of 4360)
4360 / 3 = 1453.3333333333 (the remainder is 1, so 3 is not a divisor of 4360)
...
4360 / 65 = 67.076923076923 (the remainder is 5, so 65 is not a divisor of 4360)
4360 / 66 = 66.060606060606 (the remainder is 4, so 66 is not a divisor of 4360)