It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 499, the answer is: yes, 499 is a prime number because it has only two distinct divisors: 1 and itself (499).
As a consequence, 499 is only a multiple of 1 and 499..
Since 499 is a prime number, 499 is also a deficient number, that is to say 499 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 499 without 499 itself (that is 1, by definition!).
Parity of 499
499 is an odd number, because it is not evenly divisible by 2.
Is 499 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 499 is about 22.338.
Thus, the square root of 499 is not an integer, and therefore 499 is not a square number.
Anyway, 499 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 499?
The square of a number (here 499) is the result of the product of this number (499) by itself (i.e., 499 × 499); the square of 499 is sometimes called "raising 499 to the power 2", or "499 squared".
As a consequence, 499 is the square root of 249 001.
Number of digits of 499
499 is a number with 3 digits.
What are the multiples of 499?
The multiples of 499 are all integers evenly divisible by 499, that is all numbers such that the remainder of the division by 499 is zero. There are infinitely many multiples of 499. The smallest multiples of 499 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 499 too, since 0 × 499 = 0
- 499: indeed, 499 is a multiple of itself, since 499 is evenly divisible by 499 (we have 499 / 499 = 1, so the remainder of this division is indeed zero)
- 998: indeed, 998 = 499 × 2
- 1 497: indeed, 1 497 = 499 × 3
- 1 996: indeed, 1 996 = 499 × 4
- 2 495: indeed, 2 495 = 499 × 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 499). 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 22.338). 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.