What are the divisors of 4663?

1, 4663

There is a total of 2 positive divisors.
The sum of these divisors is 4664.
The arithmetic mean is 2332.

2 odd divisors

1, 4663

How to compute the divisors of 4663?

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 4663 by each of the numbers from 1 to 4663 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)

4663 / 1 = 4663 (the remainder is 0, so 1 is a divisor of 4663)
4663 / 2 = 2331.5 (the remainder is 1, so 2 is not a divisor of 4663)
4663 / 3 = 1554.3333333333 (the remainder is 1, so 3 is not a divisor of 4663)
...
4663 / 4662 = 1.0002145002145 (the remainder is 1, so 4662 is not a divisor of 4663)
4663 / 4663 = 1 (the remainder is 0, so 4663 is a divisor of 4663)

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 4663 (i.e. 68.286162580716). 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 $\frac{N}{d} = D$ )

4663 / 1 = 4663 (the remainder is 0, so 1 and 4663 are divisors of 4663)
4663 / 2 = 2331.5 (the remainder is 1, so 2 is not a divisor of 4663)
4663 / 3 = 1554.3333333333 (the remainder is 1, so 3 is not a divisor of 4663)
...
4663 / 67 = 69.597014925373 (the remainder is 40, so 67 is not a divisor of 4663)
4663 / 68 = 68.573529411765 (the remainder is 39, so 68 is not a divisor of 4663)