It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 457, the answer is: yes, 457 is a prime number because it has only two distinct divisors: 1 and itself (457).
As a consequence, 457 is only a multiple of 1 and 457..
Since 457 is a prime number, 457 is also a deficient number, that is to say 457 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 457 without 457 itself (that is 1, by definition!).
Parity of 457
457 is an odd number, because it is not evenly divisible by 2.
Is 457 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 457 is about 21.378.
Thus, the square root of 457 is not an integer, and therefore 457 is not a square number.
Anyway, 457 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 457?
The square of a number (here 457) is the result of the product of this number (457) by itself (i.e., 457 × 457); the square of 457 is sometimes called "raising 457 to the power 2", or "457 squared".
As a consequence, 457 is the square root of 208 849.
Number of digits of 457
457 is a number with 3 digits.
What are the multiples of 457?
The multiples of 457 are all integers evenly divisible by 457, that is all numbers such that the remainder of the division by 457 is zero. There are infinitely many multiples of 457. The smallest multiples of 457 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 457 too, since 0 × 457 = 0
- 457: indeed, 457 is a multiple of itself, since 457 is evenly divisible by 457 (we have 457 / 457 = 1, so the remainder of this division is indeed zero)
- 914: indeed, 914 = 457 × 2
- 1 371: indeed, 1 371 = 457 × 3
- 1 828: indeed, 1 828 = 457 × 4
- 2 285: indeed, 2 285 = 457 × 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 457). 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 21.378). 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.