What are the divisors of 387?

1, 3, 9, 43, 129, 387

There is a total of 6 positive divisors.
The sum of these divisors is 572.
The arithmetic mean is 95.333333333333.

6 odd divisors

1, 3, 9, 43, 129, 387

How to compute the divisors of 387?

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 387 by each of the numbers from 1 to 387 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)

387 / 1 = 387 (the remainder is 0, so 1 is a divisor of 387)
387 / 2 = 193.5 (the remainder is 1, so 2 is not a divisor of 387)
387 / 3 = 129 (the remainder is 0, so 3 is a divisor of 387)
...
387 / 386 = 1.0025906735751 (the remainder is 1, so 386 is not a divisor of 387)
387 / 387 = 1 (the remainder is 0, so 387 is a divisor of 387)

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 387 (i.e. 19.672315572906). 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 $\frac{N}{d} = D$ )

387 / 1 = 387 (the remainder is 0, so 1 and 387 are divisors of 387)
387 / 2 = 193.5 (the remainder is 1, so 2 is not a divisor of 387)
387 / 3 = 129 (the remainder is 0, so 3 and 129 are divisors of 387)
...
387 / 18 = 21.5 (the remainder is 9, so 18 is not a divisor of 387)
387 / 19 = 20.368421052632 (the remainder is 7, so 19 is not a divisor of 387)