What are the divisors of 386?

1, 2, 193, 386

There is a total of 4 positive divisors.
The sum of these divisors is 582.
The arithmetic mean is 145.5.

2 even divisors

2, 386

2 odd divisors

1, 193

How to compute the divisors of 386?

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 386 by each of the numbers from 1 to 386 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)

386 / 1 = 386 (the remainder is 0, so 1 is a divisor of 386)
386 / 2 = 193 (the remainder is 0, so 2 is a divisor of 386)
386 / 3 = 128.66666666667 (the remainder is 2, so 3 is not a divisor of 386)
...
386 / 385 = 1.0025974025974 (the remainder is 1, so 385 is not a divisor of 386)
386 / 386 = 1 (the remainder is 0, so 386 is a divisor of 386)

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 386 (i.e. 19.646882704388). 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 $\frac{N}{d} = D$ )

386 / 1 = 386 (the remainder is 0, so 1 and 386 are divisors of 386)
386 / 2 = 193 (the remainder is 0, so 2 and 193 are divisors of 386)
386 / 3 = 128.66666666667 (the remainder is 2, so 3 is not a divisor of 386)
...
386 / 18 = 21.444444444444 (the remainder is 8, so 18 is not a divisor of 386)
386 / 19 = 20.315789473684 (the remainder is 6, so 19 is not a divisor of 386)