What are the divisors of 4341?

1, 3, 1447, 4341

There is a total of 4 positive divisors.
The sum of these divisors is 5792.
The arithmetic mean is 1448.

4 odd divisors

1, 3, 1447, 4341

How to compute the divisors of 4341?

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 4341 by each of the numbers from 1 to 4341 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)

4341 / 1 = 4341 (the remainder is 0, so 1 is a divisor of 4341)
4341 / 2 = 2170.5 (the remainder is 1, so 2 is not a divisor of 4341)
4341 / 3 = 1447 (the remainder is 0, so 3 is a divisor of 4341)
...
4341 / 4340 = 1.0002304147465 (the remainder is 1, so 4340 is not a divisor of 4341)
4341 / 4341 = 1 (the remainder is 0, so 4341 is a divisor of 4341)

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 4341 (i.e. 65.886265640117). 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 $\frac{N}{d} = D$ )

4341 / 1 = 4341 (the remainder is 0, so 1 and 4341 are divisors of 4341)
4341 / 2 = 2170.5 (the remainder is 1, so 2 is not a divisor of 4341)
4341 / 3 = 1447 (the remainder is 0, so 3 and 1447 are divisors of 4341)
...
4341 / 64 = 67.828125 (the remainder is 53, so 64 is not a divisor of 4341)
4341 / 65 = 66.784615384615 (the remainder is 51, so 65 is not a divisor of 4341)