What are the divisors of 4361?

1, 7, 49, 89, 623, 4361

There is a total of 6 positive divisors.
The sum of these divisors is 5130.
The arithmetic mean is 855.

6 odd divisors

1, 7, 49, 89, 623, 4361

How to compute the divisors of 4361?

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 4361 by each of the numbers from 1 to 4361 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)

4361 / 1 = 4361 (the remainder is 0, so 1 is a divisor of 4361)
4361 / 2 = 2180.5 (the remainder is 1, so 2 is not a divisor of 4361)
4361 / 3 = 1453.6666666667 (the remainder is 2, so 3 is not a divisor of 4361)
...
4361 / 4360 = 1.0002293577982 (the remainder is 1, so 4360 is not a divisor of 4361)
4361 / 4361 = 1 (the remainder is 0, so 4361 is a divisor of 4361)

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 4361 (i.e. 66.037867924396). 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 $\frac{N}{d} = D$ )

4361 / 1 = 4361 (the remainder is 0, so 1 and 4361 are divisors of 4361)
4361 / 2 = 2180.5 (the remainder is 1, so 2 is not a divisor of 4361)
4361 / 3 = 1453.6666666667 (the remainder is 2, so 3 is not a divisor of 4361)
...
4361 / 65 = 67.092307692308 (the remainder is 6, so 65 is not a divisor of 4361)
4361 / 66 = 66.075757575758 (the remainder is 5, so 66 is not a divisor of 4361)