What are the divisors of 1926?

1, 2, 3, 6, 9, 18, 107, 214, 321, 642, 963, 1926

There is a total of 12 positive divisors.
The sum of these divisors is 4212.
The arithmetic mean is 351.

6 even divisors

2, 6, 18, 214, 642, 1926

6 odd divisors

1, 3, 9, 107, 321, 963

How to compute the divisors of 1926?

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 1926 by each of the numbers from 1 to 1926 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)

1926 / 1 = 1926 (the remainder is 0, so 1 is a divisor of 1926)
1926 / 2 = 963 (the remainder is 0, so 2 is a divisor of 1926)
1926 / 3 = 642 (the remainder is 0, so 3 is a divisor of 1926)
...
1926 / 1925 = 1.0005194805195 (the remainder is 1, so 1925 is not a divisor of 1926)
1926 / 1926 = 1 (the remainder is 0, so 1926 is a divisor of 1926)

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 1926 (i.e. 43.886216514983). 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 $\frac{N}{d} = D$ )

1926 / 1 = 1926 (the remainder is 0, so 1 and 1926 are divisors of 1926)
1926 / 2 = 963 (the remainder is 0, so 2 and 963 are divisors of 1926)
1926 / 3 = 642 (the remainder is 0, so 3 and 642 are divisors of 1926)
...
1926 / 42 = 45.857142857143 (the remainder is 36, so 42 is not a divisor of 1926)
1926 / 43 = 44.790697674419 (the remainder is 34, so 43 is not a divisor of 1926)