It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 467, the answer is: yes, 467 is a prime number because it has only two distinct divisors: 1 and itself (467).
As a consequence, 467 is only a multiple of 1 and 467..
Since 467 is a prime number, 467 is also a deficient number, that is to say 467 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 467 without 467 itself (that is 1, by definition!).
Parity of 467
467 is an odd number, because it is not evenly divisible by 2.
Is 467 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 467 is about 21.610.
Thus, the square root of 467 is not an integer, and therefore 467 is not a square number.
Anyway, 467 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 467?
The square of a number (here 467) is the result of the product of this number (467) by itself (i.e., 467 × 467); the square of 467 is sometimes called "raising 467 to the power 2", or "467 squared".
As a consequence, 467 is the square root of 218 089.
Number of digits of 467
467 is a number with 3 digits.
What are the multiples of 467?
The multiples of 467 are all integers evenly divisible by 467, that is all numbers such that the remainder of the division by 467 is zero. There are infinitely many multiples of 467. The smallest multiples of 467 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 467 too, since 0 × 467 = 0
- 467: indeed, 467 is a multiple of itself, since 467 is evenly divisible by 467 (we have 467 / 467 = 1, so the remainder of this division is indeed zero)
- 934: indeed, 934 = 467 × 2
- 1 401: indeed, 1 401 = 467 × 3
- 1 868: indeed, 1 868 = 467 × 4
- 2 335: indeed, 2 335 = 467 × 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 467). 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 21.610). 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.