What are the divisors of 4683?

1, 3, 7, 21, 223, 669, 1561, 4683

There is a total of 8 positive divisors.
The sum of these divisors is 7168.
The arithmetic mean is 896.

8 odd divisors

1, 3, 7, 21, 223, 669, 1561, 4683

How to compute the divisors of 4683?

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 4683 by each of the numbers from 1 to 4683 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)

4683 / 1 = 4683 (the remainder is 0, so 1 is a divisor of 4683)
4683 / 2 = 2341.5 (the remainder is 1, so 2 is not a divisor of 4683)
4683 / 3 = 1561 (the remainder is 0, so 3 is a divisor of 4683)
...
4683 / 4682 = 1.0002135839385 (the remainder is 1, so 4682 is not a divisor of 4683)
4683 / 4683 = 1 (the remainder is 0, so 4683 is a divisor of 4683)

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 4683 (i.e. 68.432448443702). 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 $\frac{N}{d} = D$ )

4683 / 1 = 4683 (the remainder is 0, so 1 and 4683 are divisors of 4683)
4683 / 2 = 2341.5 (the remainder is 1, so 2 is not a divisor of 4683)
4683 / 3 = 1561 (the remainder is 0, so 3 and 1561 are divisors of 4683)
...
4683 / 67 = 69.89552238806 (the remainder is 60, so 67 is not a divisor of 4683)
4683 / 68 = 68.867647058824 (the remainder is 59, so 68 is not a divisor of 4683)