What are the divisors of 4331?

1, 61, 71, 4331

There is a total of 4 positive divisors.
The sum of these divisors is 4464.
The arithmetic mean is 1116.

4 odd divisors

1, 61, 71, 4331

How to compute the divisors of 4331?

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 4331 by each of the numbers from 1 to 4331 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)

4331 / 1 = 4331 (the remainder is 0, so 1 is a divisor of 4331)
4331 / 2 = 2165.5 (the remainder is 1, so 2 is not a divisor of 4331)
4331 / 3 = 1443.6666666667 (the remainder is 2, so 3 is not a divisor of 4331)
...
4331 / 4330 = 1.0002309468822 (the remainder is 1, so 4330 is not a divisor of 4331)
4331 / 4331 = 1 (the remainder is 0, so 4331 is a divisor of 4331)

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 4331 (i.e. 65.810333535092). 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 $\frac{N}{d} = D$ )

4331 / 1 = 4331 (the remainder is 0, so 1 and 4331 are divisors of 4331)
4331 / 2 = 2165.5 (the remainder is 1, so 2 is not a divisor of 4331)
4331 / 3 = 1443.6666666667 (the remainder is 2, so 3 is not a divisor of 4331)
...
4331 / 64 = 67.671875 (the remainder is 43, so 64 is not a divisor of 4331)
4331 / 65 = 66.630769230769 (the remainder is 41, so 65 is not a divisor of 4331)