It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 251, the answer is: yes, 251 is a prime number because it has only two distinct divisors: 1 and itself (251).
As a consequence, 251 is only a multiple of 1 and 251..
Since 251 is a prime number, 251 is also a deficient number, that is to say 251 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 251 without 251 itself (that is 1, by definition!).
Parity of 251
251 is an odd number, because it is not evenly divisible by 2.
Is 251 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 251 is about 15.843.
Thus, the square root of 251 is not an integer, and therefore 251 is not a square number.
Anyway, 251 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 251?
The square of a number (here 251) is the result of the product of this number (251) by itself (i.e., 251 × 251); the square of 251 is sometimes called "raising 251 to the power 2", or "251 squared".
As a consequence, 251 is the square root of 63 001.
Number of digits of 251
251 is a number with 3 digits.
What are the multiples of 251?
The multiples of 251 are all integers evenly divisible by 251, that is all numbers such that the remainder of the division by 251 is zero. There are infinitely many multiples of 251. The smallest multiples of 251 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 251 too, since 0 × 251 = 0
- 251: indeed, 251 is a multiple of itself, since 251 is evenly divisible by 251 (we have 251 / 251 = 1, so the remainder of this division is indeed zero)
- 502: indeed, 502 = 251 × 2
- 753: indeed, 753 = 251 × 3
- 1 004: indeed, 1 004 = 251 × 4
- 1 255: indeed, 1 255 = 251 × 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 251). 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 15.843). 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.