Is 449 a prime number?

449 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 449 is about 21.190.

Thus, the square root of 449 is not an integer, and therefore 449 is not a square number.

Anyway, 449 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 449) is the result of the product of this number (449) by itself (i.e., 449 × 449); the square of 449 is sometimes called "raising 449 to the power 2", or "449 squared".

The square of 449 is 201 601 because 449 × 449 = 449² = 201 601.

As a consequence, 449 is the square root of 201 601.

449 is a number with 3 digits.

The multiples of 449 are all integers evenly divisible by 449, that is all numbers such that the remainder of the division by 449 is zero. There are infinitely many multiples of 449. The smallest multiples of 449 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 449 too, since 0 × 449 = 0
• 449: indeed, 449 is a multiple of itself, since 449 is evenly divisible by 449 (we have 449 / 449 = 1, so the remainder of this division is indeed zero)
• 898: indeed, 898 = 449 × 2
• 1 347: indeed, 1 347 = 449 × 3
• 1 796: indeed, 1 796 = 449 × 4
• 2 245: indeed, 2 245 = 449 × 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 449). 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 21.190). 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: …447, 448
• Following numbers: 450, 451…

Nearest numbers from 449

• Preceding prime number: 443
• Following prime number: 457

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• 449 est-il un nombre premier ?