It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 163, the answer is: yes, 163 is a prime number because it has only two distinct divisors: 1 and itself (163).
As a consequence, 163 is only a multiple of 1 and 163..
Since 163 is a prime number, 163 is also a deficient number, that is to say 163 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 163 without 163 itself (that is 1, by definition!).
Parity of 163
163 is an odd number, because it is not evenly divisible by 2.
Is 163 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 163 is about 12.767.
Thus, the square root of 163 is not an integer, and therefore 163 is not a square number.
Anyway, 163 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 163?
The square of a number (here 163) is the result of the product of this number (163) by itself (i.e., 163 × 163); the square of 163 is sometimes called "raising 163 to the power 2", or "163 squared".
As a consequence, 163 is the square root of 26 569.
Number of digits of 163
163 is a number with 3 digits.
What are the multiples of 163?
The multiples of 163 are all integers evenly divisible by 163, that is all numbers such that the remainder of the division by 163 is zero. There are infinitely many multiples of 163. The smallest multiples of 163 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 163 too, since 0 × 163 = 0
- 163: indeed, 163 is a multiple of itself, since 163 is evenly divisible by 163 (we have 163 / 163 = 1, so the remainder of this division is indeed zero)
- 326: indeed, 326 = 163 × 2
- 489: indeed, 489 = 163 × 3
- 652: indeed, 652 = 163 × 4
- 815: indeed, 815 = 163 × 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 163). 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 12.767). 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.