What are the divisors of 4224?

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 128, 132, 176, 192, 264, 352, 384, 528, 704, 1056, 1408, 2112, 4224

There is a total of 32 positive divisors.
The sum of these divisors is 12240.
The arithmetic mean is 382.5.

28 even divisors

2, 4, 6, 8, 12, 16, 22, 24, 32, 44, 48, 64, 66, 88, 96, 128, 132, 176, 192, 264, 352, 384, 528, 704, 1056, 1408, 2112, 4224

4 odd divisors

1, 3, 11, 33

How to compute the divisors of 4224?

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 4224 by each of the numbers from 1 to 4224 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)

4224 / 1 = 4224 (the remainder is 0, so 1 is a divisor of 4224)
4224 / 2 = 2112 (the remainder is 0, so 2 is a divisor of 4224)
4224 / 3 = 1408 (the remainder is 0, so 3 is a divisor of 4224)
...
4224 / 4223 = 1.0002367984845 (the remainder is 1, so 4223 is not a divisor of 4224)
4224 / 4224 = 1 (the remainder is 0, so 4224 is a divisor of 4224)

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 4224 (i.e. 64.992307237088). 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 $\frac{N}{d} = D$ )

4224 / 1 = 4224 (the remainder is 0, so 1 and 4224 are divisors of 4224)
4224 / 2 = 2112 (the remainder is 0, so 2 and 2112 are divisors of 4224)
4224 / 3 = 1408 (the remainder is 0, so 3 and 1408 are divisors of 4224)
...
4224 / 63 = 67.047619047619 (the remainder is 3, so 63 is not a divisor of 4224)
4224 / 64 = 66 (the remainder is 0, so 64 and 66 are divisors of 4224)