What are the divisors of 385?

1, 5, 7, 11, 35, 55, 77, 385

There is a total of 8 positive divisors.
The sum of these divisors is 576.
The arithmetic mean is 72.

8 odd divisors

1, 5, 7, 11, 35, 55, 77, 385

How to compute the divisors of 385?

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 385 by each of the numbers from 1 to 385 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)

385 / 1 = 385 (the remainder is 0, so 1 is a divisor of 385)
385 / 2 = 192.5 (the remainder is 1, so 2 is not a divisor of 385)
385 / 3 = 128.33333333333 (the remainder is 1, so 3 is not a divisor of 385)
...
385 / 384 = 1.0026041666667 (the remainder is 1, so 384 is not a divisor of 385)
385 / 385 = 1 (the remainder is 0, so 385 is a divisor of 385)

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 385 (i.e. 19.621416870349). 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 $\frac{N}{d} = D$ )

385 / 1 = 385 (the remainder is 0, so 1 and 385 are divisors of 385)
385 / 2 = 192.5 (the remainder is 1, so 2 is not a divisor of 385)
385 / 3 = 128.33333333333 (the remainder is 1, so 3 is not a divisor of 385)
...
385 / 18 = 21.388888888889 (the remainder is 7, so 18 is not a divisor of 385)
385 / 19 = 20.263157894737 (the remainder is 5, so 19 is not a divisor of 385)