What are the divisors of 4343?

1, 43, 101, 4343

There is a total of 4 positive divisors.
The sum of these divisors is 4488.
The arithmetic mean is 1122.

4 odd divisors

1, 43, 101, 4343

How to compute the divisors of 4343?

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 4343 by each of the numbers from 1 to 4343 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)

4343 / 1 = 4343 (the remainder is 0, so 1 is a divisor of 4343)
4343 / 2 = 2171.5 (the remainder is 1, so 2 is not a divisor of 4343)
4343 / 3 = 1447.6666666667 (the remainder is 2, so 3 is not a divisor of 4343)
...
4343 / 4342 = 1.0002303086135 (the remainder is 1, so 4342 is not a divisor of 4343)
4343 / 4343 = 1 (the remainder is 0, so 4343 is a divisor of 4343)

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 4343 (i.e. 65.901441562382). 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 $\frac{N}{d} = D$ )

4343 / 1 = 4343 (the remainder is 0, so 1 and 4343 are divisors of 4343)
4343 / 2 = 2171.5 (the remainder is 1, so 2 is not a divisor of 4343)
4343 / 3 = 1447.6666666667 (the remainder is 2, so 3 is not a divisor of 4343)
...
4343 / 64 = 67.859375 (the remainder is 55, so 64 is not a divisor of 4343)
4343 / 65 = 66.815384615385 (the remainder is 53, so 65 is not a divisor of 4343)