What are the divisors of 4322?

1, 2, 2161, 4322

There is a total of 4 positive divisors.
The sum of these divisors is 6486.
The arithmetic mean is 1621.5.

2 even divisors

2, 4322

2 odd divisors

1, 2161

How to compute the divisors of 4322?

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 4322 by each of the numbers from 1 to 4322 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)

4322 / 1 = 4322 (the remainder is 0, so 1 is a divisor of 4322)
4322 / 2 = 2161 (the remainder is 0, so 2 is a divisor of 4322)
4322 / 3 = 1440.6666666667 (the remainder is 2, so 3 is not a divisor of 4322)
...
4322 / 4321 = 1.0002314279102 (the remainder is 1, so 4321 is not a divisor of 4322)
4322 / 4322 = 1 (the remainder is 0, so 4322 is a divisor of 4322)

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 4322 (i.e. 65.741919655574). 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 $\frac{N}{d} = D$ )

4322 / 1 = 4322 (the remainder is 0, so 1 and 4322 are divisors of 4322)
4322 / 2 = 2161 (the remainder is 0, so 2 and 2161 are divisors of 4322)
4322 / 3 = 1440.6666666667 (the remainder is 2, so 3 is not a divisor of 4322)
...
4322 / 64 = 67.53125 (the remainder is 34, so 64 is not a divisor of 4322)
4322 / 65 = 66.492307692308 (the remainder is 32, so 65 is not a divisor of 4322)