It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 431, the answer is: yes, 431 is a prime number because it has only two distinct divisors: 1 and itself (431).
As a consequence, 431 is only a multiple of 1 and 431..
Since 431 is a prime number, 431 is also a deficient number, that is to say 431 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 431 without 431 itself (that is 1, by definition!).
Parity of 431
431 is an odd number, because it is not evenly divisible by 2.
Is 431 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 431 is about 20.761.
Thus, the square root of 431 is not an integer, and therefore 431 is not a square number.
Anyway, 431 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 431?
The square of a number (here 431) is the result of the product of this number (431) by itself (i.e., 431 × 431); the square of 431 is sometimes called "raising 431 to the power 2", or "431 squared".
As a consequence, 431 is the square root of 185 761.
Number of digits of 431
431 is a number with 3 digits.
What are the multiples of 431?
The multiples of 431 are all integers evenly divisible by 431, that is all numbers such that the remainder of the division by 431 is zero. There are infinitely many multiples of 431. The smallest multiples of 431 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 431 too, since 0 × 431 = 0
- 431: indeed, 431 is a multiple of itself, since 431 is evenly divisible by 431 (we have 431 / 431 = 1, so the remainder of this division is indeed zero)
- 862: indeed, 862 = 431 × 2
- 1 293: indeed, 1 293 = 431 × 3
- 1 724: indeed, 1 724 = 431 × 4
- 2 155: indeed, 2 155 = 431 × 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 431). 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 20.761). 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.