What are the divisors of 1927?

1, 41, 47, 1927

There is a total of 4 positive divisors.
The sum of these divisors is 2016.
The arithmetic mean is 504.

4 odd divisors

1, 41, 47, 1927

How to compute the divisors of 1927?

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 1927 by each of the numbers from 1 to 1927 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)

1927 / 1 = 1927 (the remainder is 0, so 1 is a divisor of 1927)
1927 / 2 = 963.5 (the remainder is 1, so 2 is not a divisor of 1927)
1927 / 3 = 642.33333333333 (the remainder is 1, so 3 is not a divisor of 1927)
...
1927 / 1926 = 1.0005192107996 (the remainder is 1, so 1926 is not a divisor of 1927)
1927 / 1927 = 1 (the remainder is 0, so 1927 is a divisor of 1927)

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 1927 (i.e. 43.897608135296). 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 $\frac{N}{d} = D$ )

1927 / 1 = 1927 (the remainder is 0, so 1 and 1927 are divisors of 1927)
1927 / 2 = 963.5 (the remainder is 1, so 2 is not a divisor of 1927)
1927 / 3 = 642.33333333333 (the remainder is 1, so 3 is not a divisor of 1927)
...
1927 / 42 = 45.880952380952 (the remainder is 37, so 42 is not a divisor of 1927)
1927 / 43 = 44.813953488372 (the remainder is 35, so 43 is not a divisor of 1927)