It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 281, the answer is: yes, 281 is a prime number because it has only two distinct divisors: 1 and itself (281).
As a consequence, 281 is only a multiple of 1 and 281..
Since 281 is a prime number, 281 is also a deficient number, that is to say 281 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 281 without 281 itself (that is 1, by definition!).
Parity of 281
281 is an odd number, because it is not evenly divisible by 2.
Is 281 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 281 is about 16.763.
Thus, the square root of 281 is not an integer, and therefore 281 is not a square number.
Anyway, 281 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 281?
The square of a number (here 281) is the result of the product of this number (281) by itself (i.e., 281 × 281); the square of 281 is sometimes called "raising 281 to the power 2", or "281 squared".
As a consequence, 281 is the square root of 78 961.
Number of digits of 281
281 is a number with 3 digits.
What are the multiples of 281?
The multiples of 281 are all integers evenly divisible by 281, that is all numbers such that the remainder of the division by 281 is zero. There are infinitely many multiples of 281. The smallest multiples of 281 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 281 too, since 0 × 281 = 0
- 281: indeed, 281 is a multiple of itself, since 281 is evenly divisible by 281 (we have 281 / 281 = 1, so the remainder of this division is indeed zero)
- 562: indeed, 562 = 281 × 2
- 843: indeed, 843 = 281 × 3
- 1 124: indeed, 1 124 = 281 × 4
- 1 405: indeed, 1 405 = 281 × 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 281). 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 16.763). 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.