What are the divisors of 4662?

1, 2, 3, 6, 7, 9, 14, 18, 21, 37, 42, 63, 74, 111, 126, 222, 259, 333, 518, 666, 777, 1554, 2331, 4662

There is a total of 24 positive divisors.
The sum of these divisors is 11856.
The arithmetic mean is 494.

12 even divisors

2, 6, 14, 18, 42, 74, 126, 222, 518, 666, 1554, 4662

12 odd divisors

1, 3, 7, 9, 21, 37, 63, 111, 259, 333, 777, 2331

How to compute the divisors of 4662?

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 4662 by each of the numbers from 1 to 4662 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)

4662 / 1 = 4662 (the remainder is 0, so 1 is a divisor of 4662)
4662 / 2 = 2331 (the remainder is 0, so 2 is a divisor of 4662)
4662 / 3 = 1554 (the remainder is 0, so 3 is a divisor of 4662)
...
4662 / 4661 = 1.0002145462347 (the remainder is 1, so 4661 is not a divisor of 4662)
4662 / 4662 = 1 (the remainder is 0, so 4662 is a divisor of 4662)

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 4662 (i.e. 68.278840060446). 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 $\frac{N}{d} = D$ )

4662 / 1 = 4662 (the remainder is 0, so 1 and 4662 are divisors of 4662)
4662 / 2 = 2331 (the remainder is 0, so 2 and 2331 are divisors of 4662)
4662 / 3 = 1554 (the remainder is 0, so 3 and 1554 are divisors of 4662)
...
4662 / 67 = 69.582089552239 (the remainder is 39, so 67 is not a divisor of 4662)
4662 / 68 = 68.558823529412 (the remainder is 38, so 68 is not a divisor of 4662)