What are the divisors of 4428?

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 41, 54, 82, 108, 123, 164, 246, 369, 492, 738, 1107, 1476, 2214, 4428

There is a total of 24 positive divisors.
The sum of these divisors is 11760.
The arithmetic mean is 490.

16 even divisors

2, 4, 6, 12, 18, 36, 54, 82, 108, 164, 246, 492, 738, 1476, 2214, 4428

8 odd divisors

1, 3, 9, 27, 41, 123, 369, 1107

How to compute the divisors of 4428?

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 4428 by each of the numbers from 1 to 4428 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)

4428 / 1 = 4428 (the remainder is 0, so 1 is a divisor of 4428)
4428 / 2 = 2214 (the remainder is 0, so 2 is a divisor of 4428)
4428 / 3 = 1476 (the remainder is 0, so 3 is a divisor of 4428)
...
4428 / 4427 = 1.0002258866049 (the remainder is 1, so 4427 is not a divisor of 4428)
4428 / 4428 = 1 (the remainder is 0, so 4428 is a divisor of 4428)

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 4428 (i.e. 66.543219038456). 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 $\frac{N}{d} = D$ )

4428 / 1 = 4428 (the remainder is 0, so 1 and 4428 are divisors of 4428)
4428 / 2 = 2214 (the remainder is 0, so 2 and 2214 are divisors of 4428)
4428 / 3 = 1476 (the remainder is 0, so 3 and 1476 are divisors of 4428)
...
4428 / 65 = 68.123076923077 (the remainder is 8, so 65 is not a divisor of 4428)
4428 / 66 = 67.090909090909 (the remainder is 6, so 66 is not a divisor of 4428)