What are the divisors of 395?

1, 5, 79, 395

There is a total of 4 positive divisors.
The sum of these divisors is 480.
The arithmetic mean is 120.

4 odd divisors

1, 5, 79, 395

How to compute the divisors of 395?

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 395 by each of the numbers from 1 to 395 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)

395 / 1 = 395 (the remainder is 0, so 1 is a divisor of 395)
395 / 2 = 197.5 (the remainder is 1, so 2 is not a divisor of 395)
395 / 3 = 131.66666666667 (the remainder is 2, so 3 is not a divisor of 395)
...
395 / 394 = 1.002538071066 (the remainder is 1, so 394 is not a divisor of 395)
395 / 395 = 1 (the remainder is 0, so 395 is a divisor of 395)

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 395 (i.e. 19.874606914352). 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 $\frac{N}{d} = D$ )

395 / 1 = 395 (the remainder is 0, so 1 and 395 are divisors of 395)
395 / 2 = 197.5 (the remainder is 1, so 2 is not a divisor of 395)
395 / 3 = 131.66666666667 (the remainder is 2, so 3 is not a divisor of 395)
...
395 / 18 = 21.944444444444 (the remainder is 17, so 18 is not a divisor of 395)
395 / 19 = 20.789473684211 (the remainder is 15, so 19 is not a divisor of 395)