What are the divisors of 4332?

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228, 361, 722, 1083, 1444, 2166, 4332

There is a total of 18 positive divisors.
The sum of these divisors is 10668.
The arithmetic mean is 592.66666666667.

12 even divisors

2, 4, 6, 12, 38, 76, 114, 228, 722, 1444, 2166, 4332

6 odd divisors

1, 3, 19, 57, 361, 1083

How to compute the divisors of 4332?

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 4332 by each of the numbers from 1 to 4332 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)

4332 / 1 = 4332 (the remainder is 0, so 1 is a divisor of 4332)
4332 / 2 = 2166 (the remainder is 0, so 2 is a divisor of 4332)
4332 / 3 = 1444 (the remainder is 0, so 3 is a divisor of 4332)
...
4332 / 4331 = 1.0002308935581 (the remainder is 1, so 4331 is not a divisor of 4332)
4332 / 4332 = 1 (the remainder is 0, so 4332 is a divisor of 4332)

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 4332 (i.e. 65.817930687617). 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 $\frac{N}{d} = D$ )

4332 / 1 = 4332 (the remainder is 0, so 1 and 4332 are divisors of 4332)
4332 / 2 = 2166 (the remainder is 0, so 2 and 2166 are divisors of 4332)
4332 / 3 = 1444 (the remainder is 0, so 3 and 1444 are divisors of 4332)
...
4332 / 64 = 67.6875 (the remainder is 44, so 64 is not a divisor of 4332)
4332 / 65 = 66.646153846154 (the remainder is 42, so 65 is not a divisor of 4332)