What are the divisors of 4446?

1, 2, 3, 6, 9, 13, 18, 19, 26, 38, 39, 57, 78, 114, 117, 171, 234, 247, 342, 494, 741, 1482, 2223, 4446

There is a total of 24 positive divisors.
The sum of these divisors is 10920.
The arithmetic mean is 455.

12 even divisors

2, 6, 18, 26, 38, 78, 114, 234, 342, 494, 1482, 4446

12 odd divisors

1, 3, 9, 13, 19, 39, 57, 117, 171, 247, 741, 2223

How to compute the divisors of 4446?

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 4446 by each of the numbers from 1 to 4446 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)

4446 / 1 = 4446 (the remainder is 0, so 1 is a divisor of 4446)
4446 / 2 = 2223 (the remainder is 0, so 2 is a divisor of 4446)
4446 / 3 = 1482 (the remainder is 0, so 3 is a divisor of 4446)
...
4446 / 4445 = 1.0002249718785 (the remainder is 1, so 4445 is not a divisor of 4446)
4446 / 4446 = 1 (the remainder is 0, so 4446 is a divisor of 4446)

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 4446 (i.e. 66.678332312679). 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 $\frac{N}{d} = D$ )

4446 / 1 = 4446 (the remainder is 0, so 1 and 4446 are divisors of 4446)
4446 / 2 = 2223 (the remainder is 0, so 2 and 2223 are divisors of 4446)
4446 / 3 = 1482 (the remainder is 0, so 3 and 1482 are divisors of 4446)
...
4446 / 65 = 68.4 (the remainder is 26, so 65 is not a divisor of 4446)
4446 / 66 = 67.363636363636 (the remainder is 24, so 66 is not a divisor of 4446)