What are the divisors of 4440?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 37, 40, 60, 74, 111, 120, 148, 185, 222, 296, 370, 444, 555, 740, 888, 1110, 1480, 2220, 4440

There is a total of 32 positive divisors.
The sum of these divisors is 13680.
The arithmetic mean is 427.5.

24 even divisors

2, 4, 6, 8, 10, 12, 20, 24, 30, 40, 60, 74, 120, 148, 222, 296, 370, 444, 740, 888, 1110, 1480, 2220, 4440

8 odd divisors

1, 3, 5, 15, 37, 111, 185, 555

How to compute the divisors of 4440?

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 4440 by each of the numbers from 1 to 4440 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)

4440 / 1 = 4440 (the remainder is 0, so 1 is a divisor of 4440)
4440 / 2 = 2220 (the remainder is 0, so 2 is a divisor of 4440)
4440 / 3 = 1480 (the remainder is 0, so 3 is a divisor of 4440)
...
4440 / 4439 = 1.0002252759631 (the remainder is 1, so 4439 is not a divisor of 4440)
4440 / 4440 = 1 (the remainder is 0, so 4440 is a divisor of 4440)

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 4440 (i.e. 66.633324995831). 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 $\frac{N}{d} = D$ )

4440 / 1 = 4440 (the remainder is 0, so 1 and 4440 are divisors of 4440)
4440 / 2 = 2220 (the remainder is 0, so 2 and 2220 are divisors of 4440)
4440 / 3 = 1480 (the remainder is 0, so 3 and 1480 are divisors of 4440)
...
4440 / 65 = 68.307692307692 (the remainder is 20, so 65 is not a divisor of 4440)
4440 / 66 = 67.272727272727 (the remainder is 18, so 66 is not a divisor of 4440)