What are the divisors of 1917?

1, 3, 9, 27, 71, 213, 639, 1917

There is a total of 8 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 360.

8 odd divisors

1, 3, 9, 27, 71, 213, 639, 1917

How to compute the divisors of 1917?

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 1917 by each of the numbers from 1 to 1917 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)

1917 / 1 = 1917 (the remainder is 0, so 1 is a divisor of 1917)
1917 / 2 = 958.5 (the remainder is 1, so 2 is not a divisor of 1917)
1917 / 3 = 639 (the remainder is 0, so 3 is a divisor of 1917)
...
1917 / 1916 = 1.0005219206681 (the remainder is 1, so 1916 is not a divisor of 1917)
1917 / 1917 = 1 (the remainder is 0, so 1917 is a divisor of 1917)

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 1917 (i.e. 43.783558557979). 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 $\frac{N}{d} = D$ )

1917 / 1 = 1917 (the remainder is 0, so 1 and 1917 are divisors of 1917)
1917 / 2 = 958.5 (the remainder is 1, so 2 is not a divisor of 1917)
1917 / 3 = 639 (the remainder is 0, so 3 and 639 are divisors of 1917)
...
1917 / 42 = 45.642857142857 (the remainder is 27, so 42 is not a divisor of 1917)
1917 / 43 = 44.581395348837 (the remainder is 25, so 43 is not a divisor of 1917)