It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 263, the answer is: yes, 263 is a prime number because it has only two distinct divisors: 1 and itself (263).
As a consequence, 263 is only a multiple of 1 and 263..
Since 263 is a prime number, 263 is also a deficient number, that is to say 263 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 263 without 263 itself (that is 1, by definition!).
Parity of 263
263 is an odd number, because it is not evenly divisible by 2.
Is 263 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 263 is about 16.217.
Thus, the square root of 263 is not an integer, and therefore 263 is not a square number.
Anyway, 263 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 263?
The square of a number (here 263) is the result of the product of this number (263) by itself (i.e., 263 × 263); the square of 263 is sometimes called "raising 263 to the power 2", or "263 squared".
As a consequence, 263 is the square root of 69 169.
Number of digits of 263
263 is a number with 3 digits.
What are the multiples of 263?
The multiples of 263 are all integers evenly divisible by 263, that is all numbers such that the remainder of the division by 263 is zero. There are infinitely many multiples of 263. The smallest multiples of 263 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 263 too, since 0 × 263 = 0
- 263: indeed, 263 is a multiple of itself, since 263 is evenly divisible by 263 (we have 263 / 263 = 1, so the remainder of this division is indeed zero)
- 526: indeed, 526 = 263 × 2
- 789: indeed, 789 = 263 × 3
- 1 052: indeed, 1 052 = 263 × 4
- 1 315: indeed, 1 315 = 263 × 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 263). 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 16.217). 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.