Is 409 a prime number?

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

Find out more:

• What is an even 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.

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.

409 is a number with 3 digits.

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:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 409 too, since 0 × 409 = 0
• 409: indeed, 409 is a multiple of itself, since 409 is evenly divisible by 409 (we have 409 / 409 = 1, so the remainder of this division is indeed zero)
• 818: indeed, 818 = 409 × 2
• 1 227: indeed, 1 227 = 409 × 3
• 1 636: indeed, 1 636 = 409 × 4
• 2 045: indeed, 2 045 = 409 × 5
• etc.

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.

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

Nearest numbers from 409

• Preceding prime number: 401
• Following prime number: 419

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• 409 est-il un nombre premier ?