What are the divisors of 1932?

1, 2, 3, 4, 6, 7, 12, 14, 21, 23, 28, 42, 46, 69, 84, 92, 138, 161, 276, 322, 483, 644, 966, 1932

There is a total of 24 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 224.

16 even divisors

2, 4, 6, 12, 14, 28, 42, 46, 84, 92, 138, 276, 322, 644, 966, 1932

8 odd divisors

1, 3, 7, 21, 23, 69, 161, 483

How to compute the divisors of 1932?

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 1932 by each of the numbers from 1 to 1932 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)

1932 / 1 = 1932 (the remainder is 0, so 1 is a divisor of 1932)
1932 / 2 = 966 (the remainder is 0, so 2 is a divisor of 1932)
1932 / 3 = 644 (the remainder is 0, so 3 is a divisor of 1932)
...
1932 / 1931 = 1.0005178663905 (the remainder is 1, so 1931 is not a divisor of 1932)
1932 / 1932 = 1 (the remainder is 0, so 1932 is a divisor of 1932)

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 1932 (i.e. 43.954521951672). 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 $\frac{N}{d} = D$ )

1932 / 1 = 1932 (the remainder is 0, so 1 and 1932 are divisors of 1932)
1932 / 2 = 966 (the remainder is 0, so 2 and 966 are divisors of 1932)
1932 / 3 = 644 (the remainder is 0, so 3 and 644 are divisors of 1932)
...
1932 / 42 = 46 (the remainder is 0, so 42 and 46 are divisors of 1932)
1932 / 43 = 44.93023255814 (the remainder is 40, so 43 is not a divisor of 1932)