What are the divisors of 4644?

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 43, 54, 86, 108, 129, 172, 258, 387, 516, 774, 1161, 1548, 2322, 4644

There is a total of 24 positive divisors.
The sum of these divisors is 12320.
The arithmetic mean is 513.33333333333.

16 even divisors

2, 4, 6, 12, 18, 36, 54, 86, 108, 172, 258, 516, 774, 1548, 2322, 4644

8 odd divisors

1, 3, 9, 27, 43, 129, 387, 1161

How to compute the divisors of 4644?

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 4644 by each of the numbers from 1 to 4644 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)

4644 / 1 = 4644 (the remainder is 0, so 1 is a divisor of 4644)
4644 / 2 = 2322 (the remainder is 0, so 2 is a divisor of 4644)
4644 / 3 = 1548 (the remainder is 0, so 3 is a divisor of 4644)
...
4644 / 4643 = 1.0002153779884 (the remainder is 1, so 4643 is not a divisor of 4644)
4644 / 4644 = 1 (the remainder is 0, so 4644 is a divisor of 4644)

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 4644 (i.e. 68.146900149603). 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 $\frac{N}{d} = D$ )

4644 / 1 = 4644 (the remainder is 0, so 1 and 4644 are divisors of 4644)
4644 / 2 = 2322 (the remainder is 0, so 2 and 2322 are divisors of 4644)
4644 / 3 = 1548 (the remainder is 0, so 3 and 1548 are divisors of 4644)
...
4644 / 67 = 69.313432835821 (the remainder is 21, so 67 is not a divisor of 4644)
4644 / 68 = 68.294117647059 (the remainder is 20, so 68 is not a divisor of 4644)