What are the divisors of 4668?

1, 2, 3, 4, 6, 12, 389, 778, 1167, 1556, 2334, 4668

There is a total of 12 positive divisors.
The sum of these divisors is 10920.
The arithmetic mean is 910.

8 even divisors

2, 4, 6, 12, 778, 1556, 2334, 4668

4 odd divisors

1, 3, 389, 1167

How to compute the divisors of 4668?

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 4668 by each of the numbers from 1 to 4668 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)

4668 / 1 = 4668 (the remainder is 0, so 1 is a divisor of 4668)
4668 / 2 = 2334 (the remainder is 0, so 2 is a divisor of 4668)
4668 / 3 = 1556 (the remainder is 0, so 3 is a divisor of 4668)
...
4668 / 4667 = 1.0002142704093 (the remainder is 1, so 4667 is not a divisor of 4668)
4668 / 4668 = 1 (the remainder is 0, so 4668 is a divisor of 4668)

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 4668 (i.e. 68.322763410155). 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 $\frac{N}{d} = D$ )

4668 / 1 = 4668 (the remainder is 0, so 1 and 4668 are divisors of 4668)
4668 / 2 = 2334 (the remainder is 0, so 2 and 2334 are divisors of 4668)
4668 / 3 = 1556 (the remainder is 0, so 3 and 1556 are divisors of 4668)
...
4668 / 67 = 69.671641791045 (the remainder is 45, so 67 is not a divisor of 4668)
4668 / 68 = 68.647058823529 (the remainder is 44, so 68 is not a divisor of 4668)