What are the divisors of 4336?

1, 2, 4, 8, 16, 271, 542, 1084, 2168, 4336

There is a total of 10 positive divisors.
The sum of these divisors is 8432.
The arithmetic mean is 843.2.

8 even divisors

2, 4, 8, 16, 542, 1084, 2168, 4336

2 odd divisors

1, 271

How to compute the divisors of 4336?

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 4336 by each of the numbers from 1 to 4336 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)

4336 / 1 = 4336 (the remainder is 0, so 1 is a divisor of 4336)
4336 / 2 = 2168 (the remainder is 0, so 2 is a divisor of 4336)
4336 / 3 = 1445.3333333333 (the remainder is 1, so 3 is not a divisor of 4336)
...
4336 / 4335 = 1.0002306805075 (the remainder is 1, so 4335 is not a divisor of 4336)
4336 / 4336 = 1 (the remainder is 0, so 4336 is a divisor of 4336)

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 4336 (i.e. 65.848310532617). 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 $\frac{N}{d} = D$ )

4336 / 1 = 4336 (the remainder is 0, so 1 and 4336 are divisors of 4336)
4336 / 2 = 2168 (the remainder is 0, so 2 and 2168 are divisors of 4336)
4336 / 3 = 1445.3333333333 (the remainder is 1, so 3 is not a divisor of 4336)
...
4336 / 64 = 67.75 (the remainder is 48, so 64 is not a divisor of 4336)
4336 / 65 = 66.707692307692 (the remainder is 46, so 65 is not a divisor of 4336)