What are the divisors of 394?

1, 2, 197, 394

There is a total of 4 positive divisors.
The sum of these divisors is 594.
The arithmetic mean is 148.5.

2 even divisors

2, 394

2 odd divisors

1, 197

How to compute the divisors of 394?

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 394 by each of the numbers from 1 to 394 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)

394 / 1 = 394 (the remainder is 0, so 1 is a divisor of 394)
394 / 2 = 197 (the remainder is 0, so 2 is a divisor of 394)
394 / 3 = 131.33333333333 (the remainder is 1, so 3 is not a divisor of 394)
...
394 / 393 = 1.0025445292621 (the remainder is 1, so 393 is not a divisor of 394)
394 / 394 = 1 (the remainder is 0, so 394 is a divisor of 394)

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 394 (i.e. 19.849433241279). 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 $\frac{N}{d} = D$ )

394 / 1 = 394 (the remainder is 0, so 1 and 394 are divisors of 394)
394 / 2 = 197 (the remainder is 0, so 2 and 197 are divisors of 394)
394 / 3 = 131.33333333333 (the remainder is 1, so 3 is not a divisor of 394)
...
394 / 18 = 21.888888888889 (the remainder is 16, so 18 is not a divisor of 394)
394 / 19 = 20.736842105263 (the remainder is 14, so 19 is not a divisor of 394)