What are the divisors of 4664?

1, 2, 4, 8, 11, 22, 44, 53, 88, 106, 212, 424, 583, 1166, 2332, 4664

There is a total of 16 positive divisors.
The sum of these divisors is 9720.
The arithmetic mean is 607.5.

12 even divisors

2, 4, 8, 22, 44, 88, 106, 212, 424, 1166, 2332, 4664

4 odd divisors

1, 11, 53, 583

How to compute the divisors of 4664?

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 4664 by each of the numbers from 1 to 4664 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)

4664 / 1 = 4664 (the remainder is 0, so 1 is a divisor of 4664)
4664 / 2 = 2332 (the remainder is 0, so 2 is a divisor of 4664)
4664 / 3 = 1554.6666666667 (the remainder is 2, so 3 is not a divisor of 4664)
...
4664 / 4663 = 1.000214454214 (the remainder is 1, so 4663 is not a divisor of 4664)
4664 / 4664 = 1 (the remainder is 0, so 4664 is a divisor of 4664)

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 4664 (i.e. 68.293484315855). 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 $\frac{N}{d} = D$ )

4664 / 1 = 4664 (the remainder is 0, so 1 and 4664 are divisors of 4664)
4664 / 2 = 2332 (the remainder is 0, so 2 and 2332 are divisors of 4664)
4664 / 3 = 1554.6666666667 (the remainder is 2, so 3 is not a divisor of 4664)
...
4664 / 67 = 69.611940298507 (the remainder is 41, so 67 is not a divisor of 4664)
4664 / 68 = 68.588235294118 (the remainder is 40, so 68 is not a divisor of 4664)