What are the divisors of 381?

1, 3, 127, 381

There is a total of 4 positive divisors.
The sum of these divisors is 512.
The arithmetic mean is 128.

4 odd divisors

1, 3, 127, 381

How to compute the divisors of 381?

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 381 by each of the numbers from 1 to 381 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)

381 / 1 = 381 (the remainder is 0, so 1 is a divisor of 381)
381 / 2 = 190.5 (the remainder is 1, so 2 is not a divisor of 381)
381 / 3 = 127 (the remainder is 0, so 3 is a divisor of 381)
...
381 / 380 = 1.0026315789474 (the remainder is 1, so 380 is not a divisor of 381)
381 / 381 = 1 (the remainder is 0, so 381 is a divisor of 381)

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 381 (i.e. 19.519221295943). 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 $\frac{N}{d} = D$ )

381 / 1 = 381 (the remainder is 0, so 1 and 381 are divisors of 381)
381 / 2 = 190.5 (the remainder is 1, so 2 is not a divisor of 381)
381 / 3 = 127 (the remainder is 0, so 3 and 127 are divisors of 381)
...
381 / 18 = 21.166666666667 (the remainder is 3, so 18 is not a divisor of 381)
381 / 19 = 20.052631578947 (the remainder is 1, so 19 is not a divisor of 381)