What are the divisors of 4638?

1, 2, 3, 6, 773, 1546, 2319, 4638

There is a total of 8 positive divisors.
The sum of these divisors is 9288.
The arithmetic mean is 1161.

4 even divisors

2, 6, 1546, 4638

4 odd divisors

1, 3, 773, 2319

How to compute the divisors of 4638?

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 4638 by each of the numbers from 1 to 4638 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)

4638 / 1 = 4638 (the remainder is 0, so 1 is a divisor of 4638)
4638 / 2 = 2319 (the remainder is 0, so 2 is a divisor of 4638)
4638 / 3 = 1546 (the remainder is 0, so 3 is a divisor of 4638)
...
4638 / 4637 = 1.0002156566746 (the remainder is 1, so 4637 is not a divisor of 4638)
4638 / 4638 = 1 (the remainder is 0, so 4638 is a divisor of 4638)

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 4638 (i.e. 68.102863375926). 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 $\frac{N}{d} = D$ )

4638 / 1 = 4638 (the remainder is 0, so 1 and 4638 are divisors of 4638)
4638 / 2 = 2319 (the remainder is 0, so 2 and 2319 are divisors of 4638)
4638 / 3 = 1546 (the remainder is 0, so 3 and 1546 are divisors of 4638)
...
4638 / 67 = 69.223880597015 (the remainder is 15, so 67 is not a divisor of 4638)
4638 / 68 = 68.205882352941 (the remainder is 14, so 68 is not a divisor of 4638)