What are the divisors of 1930?

1, 2, 5, 10, 193, 386, 965, 1930

There is a total of 8 positive divisors.
The sum of these divisors is 3492.
The arithmetic mean is 436.5.

4 even divisors

2, 10, 386, 1930

4 odd divisors

1, 5, 193, 965

How to compute the divisors of 1930?

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 1930 by each of the numbers from 1 to 1930 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)

1930 / 1 = 1930 (the remainder is 0, so 1 is a divisor of 1930)
1930 / 2 = 965 (the remainder is 0, so 2 is a divisor of 1930)
1930 / 3 = 643.33333333333 (the remainder is 1, so 3 is not a divisor of 1930)
...
1930 / 1929 = 1.0005184033178 (the remainder is 1, so 1929 is not a divisor of 1930)
1930 / 1930 = 1 (the remainder is 0, so 1930 is a divisor of 1930)

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 1930 (i.e. 43.931765272978). 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 $\frac{N}{d} = D$ )

1930 / 1 = 1930 (the remainder is 0, so 1 and 1930 are divisors of 1930)
1930 / 2 = 965 (the remainder is 0, so 2 and 965 are divisors of 1930)
1930 / 3 = 643.33333333333 (the remainder is 1, so 3 is not a divisor of 1930)
...
1930 / 42 = 45.952380952381 (the remainder is 40, so 42 is not a divisor of 1930)
1930 / 43 = 44.883720930233 (the remainder is 38, so 43 is not a divisor of 1930)