What are the divisors of 4391?

1, 4391

There is a total of 2 positive divisors.
The sum of these divisors is 4392.
The arithmetic mean is 2196.

2 odd divisors

1, 4391

How to compute the divisors of 4391?

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 4391 by each of the numbers from 1 to 4391 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)

4391 / 1 = 4391 (the remainder is 0, so 1 is a divisor of 4391)
4391 / 2 = 2195.5 (the remainder is 1, so 2 is not a divisor of 4391)
4391 / 3 = 1463.6666666667 (the remainder is 2, so 3 is not a divisor of 4391)
...
4391 / 4390 = 1.0002277904328 (the remainder is 1, so 4390 is not a divisor of 4391)
4391 / 4391 = 1 (the remainder is 0, so 4391 is a divisor of 4391)

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 4391 (i.e. 66.264621028117). 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 $\frac{N}{d} = D$ )

4391 / 1 = 4391 (the remainder is 0, so 1 and 4391 are divisors of 4391)
4391 / 2 = 2195.5 (the remainder is 1, so 2 is not a divisor of 4391)
4391 / 3 = 1463.6666666667 (the remainder is 2, so 3 is not a divisor of 4391)
...
4391 / 65 = 67.553846153846 (the remainder is 36, so 65 is not a divisor of 4391)
4391 / 66 = 66.530303030303 (the remainder is 35, so 66 is not a divisor of 4391)