What are the divisors of 1922?

1, 2, 31, 62, 961, 1922

There is a total of 6 positive divisors.
The sum of these divisors is 2979.
The arithmetic mean is 496.5.

3 even divisors

2, 62, 1922

3 odd divisors

1, 31, 961

How to compute the divisors of 1922?

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 1922 by each of the numbers from 1 to 1922 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)

1922 / 1 = 1922 (the remainder is 0, so 1 is a divisor of 1922)
1922 / 2 = 961 (the remainder is 0, so 2 is a divisor of 1922)
1922 / 3 = 640.66666666667 (the remainder is 2, so 3 is not a divisor of 1922)
...
1922 / 1921 = 1.0005205622072 (the remainder is 1, so 1921 is not a divisor of 1922)
1922 / 1922 = 1 (the remainder is 0, so 1922 is a divisor of 1922)

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 1922 (i.e. 43.840620433566). 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 $\frac{N}{d} = D$ )

1922 / 1 = 1922 (the remainder is 0, so 1 and 1922 are divisors of 1922)
1922 / 2 = 961 (the remainder is 0, so 2 and 961 are divisors of 1922)
1922 / 3 = 640.66666666667 (the remainder is 2, so 3 is not a divisor of 1922)
...
1922 / 42 = 45.761904761905 (the remainder is 32, so 42 is not a divisor of 1922)
1922 / 43 = 44.697674418605 (the remainder is 30, so 43 is not a divisor of 1922)