What are the divisors of 4416?

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 64, 69, 92, 96, 138, 184, 192, 276, 368, 552, 736, 1104, 1472, 2208, 4416

There is a total of 28 positive divisors.
The sum of these divisors is 12192.
The arithmetic mean is 435.42857142857.

24 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 46, 48, 64, 92, 96, 138, 184, 192, 276, 368, 552, 736, 1104, 1472, 2208, 4416

4 odd divisors

1, 3, 23, 69

How to compute the divisors of 4416?

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 4416 by each of the numbers from 1 to 4416 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)

4416 / 1 = 4416 (the remainder is 0, so 1 is a divisor of 4416)
4416 / 2 = 2208 (the remainder is 0, so 2 is a divisor of 4416)
4416 / 3 = 1472 (the remainder is 0, so 3 is a divisor of 4416)
...
4416 / 4415 = 1.0002265005663 (the remainder is 1, so 4415 is not a divisor of 4416)
4416 / 4416 = 1 (the remainder is 0, so 4416 is a divisor of 4416)

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 4416 (i.e. 66.452990903345). 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 $\frac{N}{d} = D$ )

4416 / 1 = 4416 (the remainder is 0, so 1 and 4416 are divisors of 4416)
4416 / 2 = 2208 (the remainder is 0, so 2 and 2208 are divisors of 4416)
4416 / 3 = 1472 (the remainder is 0, so 3 and 1472 are divisors of 4416)
...
4416 / 65 = 67.938461538462 (the remainder is 61, so 65 is not a divisor of 4416)
4416 / 66 = 66.909090909091 (the remainder is 60, so 66 is not a divisor of 4416)