What are the divisors of 927?

1, 3, 9, 103, 309, 927

There is a total of 6 positive divisors.
The sum of these divisors is 1352.
The arithmetic mean is 225.33333333333.

6 odd divisors

1, 3, 9, 103, 309, 927

How to compute the divisors of 927?

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 927 by each of the numbers from 1 to 927 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)

927 / 1 = 927 (the remainder is 0, so 1 is a divisor of 927)
927 / 2 = 463.5 (the remainder is 1, so 2 is not a divisor of 927)
927 / 3 = 309 (the remainder is 0, so 3 is a divisor of 927)
...
927 / 926 = 1.0010799136069 (the remainder is 1, so 926 is not a divisor of 927)
927 / 927 = 1 (the remainder is 0, so 927 is a divisor of 927)

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 927 (i.e. 30.446674695277). 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 $\frac{N}{d} = D$ )

927 / 1 = 927 (the remainder is 0, so 1 and 927 are divisors of 927)
927 / 2 = 463.5 (the remainder is 1, so 2 is not a divisor of 927)
927 / 3 = 309 (the remainder is 0, so 3 and 309 are divisors of 927)
...
927 / 29 = 31.965517241379 (the remainder is 28, so 29 is not a divisor of 927)
927 / 30 = 30.9 (the remainder is 27, so 30 is not a divisor of 927)