What are the divisors of 4666?

1, 2, 2333, 4666

There is a total of 4 positive divisors.
The sum of these divisors is 7002.
The arithmetic mean is 1750.5.

2 even divisors

2, 4666

2 odd divisors

1, 2333

How to compute the divisors of 4666?

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 4666 by each of the numbers from 1 to 4666 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)

4666 / 1 = 4666 (the remainder is 0, so 1 is a divisor of 4666)
4666 / 2 = 2333 (the remainder is 0, so 2 is a divisor of 4666)
4666 / 3 = 1555.3333333333 (the remainder is 1, so 3 is not a divisor of 4666)
...
4666 / 4665 = 1.0002143622722 (the remainder is 1, so 4665 is not a divisor of 4666)
4666 / 4666 = 1 (the remainder is 0, so 4666 is a divisor of 4666)

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 4666 (i.e. 68.308125431752). 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 $\frac{N}{d} = D$ )

4666 / 1 = 4666 (the remainder is 0, so 1 and 4666 are divisors of 4666)
4666 / 2 = 2333 (the remainder is 0, so 2 and 2333 are divisors of 4666)
4666 / 3 = 1555.3333333333 (the remainder is 1, so 3 is not a divisor of 4666)
...
4666 / 67 = 69.641791044776 (the remainder is 43, so 67 is not a divisor of 4666)
4666 / 68 = 68.617647058824 (the remainder is 42, so 68 is not a divisor of 4666)