What are the divisors of 4328?

1, 2, 4, 8, 541, 1082, 2164, 4328

There is a total of 8 positive divisors.
The sum of these divisors is 8130.
The arithmetic mean is 1016.25.

6 even divisors

2, 4, 8, 1082, 2164, 4328

2 odd divisors

1, 541

How to compute the divisors of 4328?

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 4328 by each of the numbers from 1 to 4328 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)

4328 / 1 = 4328 (the remainder is 0, so 1 is a divisor of 4328)
4328 / 2 = 2164 (the remainder is 0, so 2 is a divisor of 4328)
4328 / 3 = 1442.6666666667 (the remainder is 2, so 3 is not a divisor of 4328)
...
4328 / 4327 = 1.0002311070025 (the remainder is 1, so 4327 is not a divisor of 4328)
4328 / 4328 = 1 (the remainder is 0, so 4328 is a divisor of 4328)

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 4328 (i.e. 65.787536813594). 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 $\frac{N}{d} = D$ )

4328 / 1 = 4328 (the remainder is 0, so 1 and 4328 are divisors of 4328)
4328 / 2 = 2164 (the remainder is 0, so 2 and 2164 are divisors of 4328)
4328 / 3 = 1442.6666666667 (the remainder is 2, so 3 is not a divisor of 4328)
...
4328 / 64 = 67.625 (the remainder is 40, so 64 is not a divisor of 4328)
4328 / 65 = 66.584615384615 (the remainder is 38, so 65 is not a divisor of 4328)