It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 463, the answer is: yes, 463 is a prime number because it has only two distinct divisors: 1 and itself (463).
As a consequence, 463 is only a multiple of 1 and 463..
Since 463 is a prime number, 463 is also a deficient number, that is to say 463 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 463 without 463 itself (that is 1, by definition!).
Parity of 463
463 is an odd number, because it is not evenly divisible by 2.
Is 463 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 463 is about 21.517.
Thus, the square root of 463 is not an integer, and therefore 463 is not a square number.
Anyway, 463 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 463?
The square of a number (here 463) is the result of the product of this number (463) by itself (i.e., 463 × 463); the square of 463 is sometimes called "raising 463 to the power 2", or "463 squared".
As a consequence, 463 is the square root of 214 369.
Number of digits of 463
463 is a number with 3 digits.
What are the multiples of 463?
The multiples of 463 are all integers evenly divisible by 463, that is all numbers such that the remainder of the division by 463 is zero. There are infinitely many multiples of 463. The smallest multiples of 463 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 463 too, since 0 × 463 = 0
- 463: indeed, 463 is a multiple of itself, since 463 is evenly divisible by 463 (we have 463 / 463 = 1, so the remainder of this division is indeed zero)
- 926: indeed, 926 = 463 × 2
- 1 389: indeed, 1 389 = 463 × 3
- 1 852: indeed, 1 852 = 463 × 4
- 2 315: indeed, 2 315 = 463 × 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 463). 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 21.517). 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.