What are the divisors of 1332?

1, 2, 3, 4, 6, 9, 12, 18, 36, 37, 74, 111, 148, 222, 333, 444, 666, 1332

There is a total of 18 positive divisors.
The sum of these divisors is 3458.
The arithmetic mean is 192.11111111111.

12 even divisors

2, 4, 6, 12, 18, 36, 74, 148, 222, 444, 666, 1332

6 odd divisors

1, 3, 9, 37, 111, 333

How to compute the divisors of 1332?

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 1332 by each of the numbers from 1 to 1332 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)

1332 / 1 = 1332 (the remainder is 0, so 1 is a divisor of 1332)
1332 / 2 = 666 (the remainder is 0, so 2 is a divisor of 1332)
1332 / 3 = 444 (the remainder is 0, so 3 is a divisor of 1332)
...
1332 / 1331 = 1.0007513148009 (the remainder is 1, so 1331 is not a divisor of 1332)
1332 / 1332 = 1 (the remainder is 0, so 1332 is a divisor of 1332)

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 1332 (i.e. 36.496575181789). 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 $\frac{N}{d} = D$ )

1332 / 1 = 1332 (the remainder is 0, so 1 and 1332 are divisors of 1332)
1332 / 2 = 666 (the remainder is 0, so 2 and 666 are divisors of 1332)
1332 / 3 = 444 (the remainder is 0, so 3 and 444 are divisors of 1332)
...
1332 / 35 = 38.057142857143 (the remainder is 2, so 35 is not a divisor of 1332)
1332 / 36 = 37 (the remainder is 0, so 36 and 37 are divisors of 1332)