What are the divisors of 1914?

1, 2, 3, 6, 11, 22, 29, 33, 58, 66, 87, 174, 319, 638, 957, 1914

There is a total of 16 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 270.

8 even divisors

2, 6, 22, 58, 66, 174, 638, 1914

8 odd divisors

1, 3, 11, 29, 33, 87, 319, 957

How to compute the divisors of 1914?

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 1914 by each of the numbers from 1 to 1914 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)

1914 / 1 = 1914 (the remainder is 0, so 1 is a divisor of 1914)
1914 / 2 = 957 (the remainder is 0, so 2 is a divisor of 1914)
1914 / 3 = 638 (the remainder is 0, so 3 is a divisor of 1914)
...
1914 / 1913 = 1.0005227391532 (the remainder is 1, so 1913 is not a divisor of 1914)
1914 / 1914 = 1 (the remainder is 0, so 1914 is a divisor of 1914)

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 1914 (i.e. 43.749285708455). 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 $\frac{N}{d} = D$ )

1914 / 1 = 1914 (the remainder is 0, so 1 and 1914 are divisors of 1914)
1914 / 2 = 957 (the remainder is 0, so 2 and 957 are divisors of 1914)
1914 / 3 = 638 (the remainder is 0, so 3 and 638 are divisors of 1914)
...
1914 / 42 = 45.571428571429 (the remainder is 24, so 42 is not a divisor of 1914)
1914 / 43 = 44.511627906977 (the remainder is 22, so 43 is not a divisor of 1914)