What are the divisors of 4349?

1, 4349

There is a total of 2 positive divisors.
The sum of these divisors is 4350.
The arithmetic mean is 2175.

2 odd divisors

1, 4349

How to compute the divisors of 4349?

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 4349 by each of the numbers from 1 to 4349 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)

4349 / 1 = 4349 (the remainder is 0, so 1 is a divisor of 4349)
4349 / 2 = 2174.5 (the remainder is 1, so 2 is not a divisor of 4349)
4349 / 3 = 1449.6666666667 (the remainder is 2, so 3 is not a divisor of 4349)
...
4349 / 4348 = 1.0002299908004 (the remainder is 1, so 4348 is not a divisor of 4349)
4349 / 4349 = 1 (the remainder is 0, so 4349 is a divisor of 4349)

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 4349 (i.e. 65.94694837519). 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 $\frac{N}{d} = D$ )

4349 / 1 = 4349 (the remainder is 0, so 1 and 4349 are divisors of 4349)
4349 / 2 = 2174.5 (the remainder is 1, so 2 is not a divisor of 4349)
4349 / 3 = 1449.6666666667 (the remainder is 2, so 3 is not a divisor of 4349)
...
4349 / 64 = 67.953125 (the remainder is 61, so 64 is not a divisor of 4349)
4349 / 65 = 66.907692307692 (the remainder is 59, so 65 is not a divisor of 4349)