What are the divisors of 4347?

1, 3, 7, 9, 21, 23, 27, 63, 69, 161, 189, 207, 483, 621, 1449, 4347

There is a total of 16 positive divisors.
The sum of these divisors is 7680.
The arithmetic mean is 480.

16 odd divisors

1, 3, 7, 9, 21, 23, 27, 63, 69, 161, 189, 207, 483, 621, 1449, 4347

How to compute the divisors of 4347?

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 4347 by each of the numbers from 1 to 4347 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)

4347 / 1 = 4347 (the remainder is 0, so 1 is a divisor of 4347)
4347 / 2 = 2173.5 (the remainder is 1, so 2 is not a divisor of 4347)
4347 / 3 = 1449 (the remainder is 0, so 3 is a divisor of 4347)
...
4347 / 4346 = 1.0002300966406 (the remainder is 1, so 4346 is not a divisor of 4347)
4347 / 4347 = 1 (the remainder is 0, so 4347 is a divisor of 4347)

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 4347 (i.e. 65.931782927508). 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 $\frac{N}{d} = D$ )

4347 / 1 = 4347 (the remainder is 0, so 1 and 4347 are divisors of 4347)
4347 / 2 = 2173.5 (the remainder is 1, so 2 is not a divisor of 4347)
4347 / 3 = 1449 (the remainder is 0, so 3 and 1449 are divisors of 4347)
...
4347 / 64 = 67.921875 (the remainder is 59, so 64 is not a divisor of 4347)
4347 / 65 = 66.876923076923 (the remainder is 57, so 65 is not a divisor of 4347)