What are the divisors of 4382?

1, 2, 7, 14, 313, 626, 2191, 4382

There is a total of 8 positive divisors.
The sum of these divisors is 7536.
The arithmetic mean is 942.

4 even divisors

2, 14, 626, 4382

4 odd divisors

1, 7, 313, 2191

How to compute the divisors of 4382?

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 4382 by each of the numbers from 1 to 4382 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)

4382 / 1 = 4382 (the remainder is 0, so 1 is a divisor of 4382)
4382 / 2 = 2191 (the remainder is 0, so 2 is a divisor of 4382)
4382 / 3 = 1460.6666666667 (the remainder is 2, so 3 is not a divisor of 4382)
...
4382 / 4381 = 1.0002282583885 (the remainder is 1, so 4381 is not a divisor of 4382)
4382 / 4382 = 1 (the remainder is 0, so 4382 is a divisor of 4382)

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 4382 (i.e. 66.196676653741). 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 $\frac{N}{d} = D$ )

4382 / 1 = 4382 (the remainder is 0, so 1 and 4382 are divisors of 4382)
4382 / 2 = 2191 (the remainder is 0, so 2 and 2191 are divisors of 4382)
4382 / 3 = 1460.6666666667 (the remainder is 2, so 3 is not a divisor of 4382)
...
4382 / 65 = 67.415384615385 (the remainder is 27, so 65 is not a divisor of 4382)
4382 / 66 = 66.393939393939 (the remainder is 26, so 66 is not a divisor of 4382)