What are the divisors of 4304?

1, 2, 4, 8, 16, 269, 538, 1076, 2152, 4304

There is a total of 10 positive divisors.
The sum of these divisors is 8370.
The arithmetic mean is 837.

8 even divisors

2, 4, 8, 16, 538, 1076, 2152, 4304

2 odd divisors

1, 269

How to compute the divisors of 4304?

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 4304 by each of the numbers from 1 to 4304 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)

4304 / 1 = 4304 (the remainder is 0, so 1 is a divisor of 4304)
4304 / 2 = 2152 (the remainder is 0, so 2 is a divisor of 4304)
4304 / 3 = 1434.6666666667 (the remainder is 2, so 3 is not a divisor of 4304)
...
4304 / 4303 = 1.0002323960028 (the remainder is 1, so 4303 is not a divisor of 4304)
4304 / 4304 = 1 (the remainder is 0, so 4304 is a divisor of 4304)

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 4304 (i.e. 65.604877867427). 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 $\frac{N}{d} = D$ )

4304 / 1 = 4304 (the remainder is 0, so 1 and 4304 are divisors of 4304)
4304 / 2 = 2152 (the remainder is 0, so 2 and 2152 are divisors of 4304)
4304 / 3 = 1434.6666666667 (the remainder is 2, so 3 is not a divisor of 4304)
...
4304 / 64 = 67.25 (the remainder is 16, so 64 is not a divisor of 4304)
4304 / 65 = 66.215384615385 (the remainder is 14, so 65 is not a divisor of 4304)