It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 449, the answer is: yes, 449 is a prime number because it has only two distinct divisors: 1 and itself (449).
As a consequence, 449 is only a multiple of 1 and 449..
Since 449 is a prime number, 449 is also a deficient number, that is to say 449 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 449 without 449 itself (that is 1, by definition!).
Parity of 449
449 is an odd number, because it is not evenly divisible by 2.
Is 449 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 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.
What is the square number of 449?
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".
As a consequence, 449 is the square root of 201 601.
Number of digits of 449
449 is a number with 3 digits.
What are the multiples of 449?
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
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 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.