What are the divisors of 4381?

1, 13, 337, 4381

There is a total of 4 positive divisors.
The sum of these divisors is 4732.
The arithmetic mean is 1183.

4 odd divisors

1, 13, 337, 4381

How to compute the divisors of 4381?

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 4381 by each of the numbers from 1 to 4381 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)

4381 / 1 = 4381 (the remainder is 0, so 1 is a divisor of 4381)
4381 / 2 = 2190.5 (the remainder is 1, so 2 is not a divisor of 4381)
4381 / 3 = 1460.3333333333 (the remainder is 1, so 3 is not a divisor of 4381)
...
4381 / 4380 = 1.0002283105023 (the remainder is 1, so 4380 is not a divisor of 4381)
4381 / 4381 = 1 (the remainder is 0, so 4381 is a divisor of 4381)

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 4381 (i.e. 66.189122973492). 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 $\frac{N}{d} = D$ )

4381 / 1 = 4381 (the remainder is 0, so 1 and 4381 are divisors of 4381)
4381 / 2 = 2190.5 (the remainder is 1, so 2 is not a divisor of 4381)
4381 / 3 = 1460.3333333333 (the remainder is 1, so 3 is not a divisor of 4381)
...
4381 / 65 = 67.4 (the remainder is 26, so 65 is not a divisor of 4381)
4381 / 66 = 66.378787878788 (the remainder is 25, so 66 is not a divisor of 4381)