Is 409 a prime number? What are the divisors of 409?

## Parity of 409

409 is an odd number, because it is not evenly divisible by 2.

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## Is 409 a perfect square number?

A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 409 is about 20.224.

Thus, the square root of 409 is not an integer, and therefore 409 is not a square number.

Anyway, 409 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 409?

The square of a number (here 409) is the result of the product of this number (409) by itself (i.e., 409 × 409); the square of 409 is sometimes called "raising 409 to the power 2", or "409 squared".

The square of 409 is 167 281 because 409 × 409 = 4092 = 167 281.

As a consequence, 409 is the square root of 167 281.

## Number of digits of 409

409 is a number with 3 digits.

## What are the multiples of 409?

The multiples of 409 are all integers evenly divisible by 409, that is all numbers such that the remainder of the division by 409 is zero. There are infinitely many multiples of 409. The smallest multiples of 409 are:

## How to determine whether an integer is a prime number?

To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 409). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 20.224). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.

More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.

## Numbers near 409

• Preceding numbers: …407, 408
• Following numbers: 410, 411

### Nearest numbers from 409

• Preceding prime number: 401
• Following prime number: 419
Find out whether some integer is a prime number