What are the divisors of 1934?

1, 2, 967, 1934

There is a total of 4 positive divisors.
The sum of these divisors is 2904.
The arithmetic mean is 726.

2 even divisors

2, 1934

2 odd divisors

1, 967

How to compute the divisors of 1934?

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 1934 by each of the numbers from 1 to 1934 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)

1934 / 1 = 1934 (the remainder is 0, so 1 is a divisor of 1934)
1934 / 2 = 967 (the remainder is 0, so 2 is a divisor of 1934)
1934 / 3 = 644.66666666667 (the remainder is 2, so 3 is not a divisor of 1934)
...
1934 / 1933 = 1.0005173305742 (the remainder is 1, so 1933 is not a divisor of 1934)
1934 / 1934 = 1 (the remainder is 0, so 1934 is a divisor of 1934)

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 1934 (i.e. 43.977266854592). 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 $\frac{N}{d} = D$ )

1934 / 1 = 1934 (the remainder is 0, so 1 and 1934 are divisors of 1934)
1934 / 2 = 967 (the remainder is 0, so 2 and 967 are divisors of 1934)
1934 / 3 = 644.66666666667 (the remainder is 2, so 3 is not a divisor of 1934)
...
1934 / 42 = 46.047619047619 (the remainder is 2, so 42 is not a divisor of 1934)
1934 / 43 = 44.976744186047 (the remainder is 42, so 43 is not a divisor of 1934)