What are the divisors of 1910?

1, 2, 5, 10, 191, 382, 955, 1910

There is a total of 8 positive divisors.
The sum of these divisors is 3456.
The arithmetic mean is 432.

4 even divisors

2, 10, 382, 1910

4 odd divisors

1, 5, 191, 955

How to compute the divisors of 1910?

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 1910 by each of the numbers from 1 to 1910 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)

1910 / 1 = 1910 (the remainder is 0, so 1 is a divisor of 1910)
1910 / 2 = 955 (the remainder is 0, so 2 is a divisor of 1910)
1910 / 3 = 636.66666666667 (the remainder is 2, so 3 is not a divisor of 1910)
...
1910 / 1909 = 1.0005238344683 (the remainder is 1, so 1909 is not a divisor of 1910)
1910 / 1910 = 1 (the remainder is 0, so 1910 is a divisor of 1910)

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 1910 (i.e. 43.703546766824). 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 $\frac{N}{d} = D$ )

1910 / 1 = 1910 (the remainder is 0, so 1 and 1910 are divisors of 1910)
1910 / 2 = 955 (the remainder is 0, so 2 and 955 are divisors of 1910)
1910 / 3 = 636.66666666667 (the remainder is 2, so 3 is not a divisor of 1910)
...
1910 / 42 = 45.47619047619 (the remainder is 20, so 42 is not a divisor of 1910)
1910 / 43 = 44.418604651163 (the remainder is 18, so 43 is not a divisor of 1910)