# Divisors of 409

## Divisors of 409

The list of all positive divisors (that is, the list of all integers that divide 22) is as follows :

Accordingly:

409 is multiplo of 1

409 has 1 positive divisors

## Parity of 409

409is an odd number,as it is not divisible by 2

## The factors for 409

The factors for 409 are all the numbers between -409 and 409 , which divide 409 without leaving any remainder. Since 409 divided by -409 is an integer, -409 is a factor of 409 .

Since 409 divided by -409 is a whole number, -409 is a factor of 409

Since 409 divided by -1 is a whole number, -1 is a factor of 409

Since 409 divided by 1 is a whole number, 1 is a factor of 409

## What are the multiples of 409?

Multiples of 409 are all integers divisible by 409 , i.e. the remainder of the full division by 409 is zero. There are infinite multiples of 409. The smallest multiples of 409 are:

0 : in fact, 0 is divisible by any integer, so it is also a multiple of 409 since 0 × 409 = 0

409 : in fact, 409 is a multiple of itself, since 409 is divisible by 409 (it was 409 / 409 = 1, so the rest of this division is zero)

818: in fact, 818 = 409 × 2

1227: in fact, 1227 = 409 × 3

1636: in fact, 1636 = 409 × 4

2045: in fact, 2045 = 409 × 5

etc.

## Is 409 a prime number?

It is possible to determine using mathematical techniques whether an integer is prime or not.

for 409, the answer is: yes, 409 is a prime number because it only has two different divisors: 1 and itself (409).

## How do you determine if a number is prime?

To know the primality of an integer, we can use several algorithms. The most naive is to try all divisors below the number you want to know if it is prime (in our case 409). We can already eliminate even numbers bigger than 2 (then 4 , 6 , 8 ...). Besides, we can stop at the square root of the number in question (here 20.224 ). Historically, the Eratosthenes screen (which dates back to Antiquity) uses this technique relatively effectively.

More modern techniques include the Atkin screen, probabilistic tests, or the cyclotomic test.