It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 461, the answer is: yes, 461 is a prime number because it has only two distinct divisors: 1 and itself (461).
As a consequence, 461 is only a multiple of 1 and 461..
Since 461 is a prime number, 461 is also a deficient number, that is to say 461 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 461 without 461 itself (that is 1, by definition!).
Parity of 461
461 is an odd number, because it is not evenly divisible by 2.
Is 461 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 461 is about 21.471.
Thus, the square root of 461 is not an integer, and therefore 461 is not a square number.
Anyway, 461 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 461?
The square of a number (here 461) is the result of the product of this number (461) by itself (i.e., 461 × 461); the square of 461 is sometimes called "raising 461 to the power 2", or "461 squared".
As a consequence, 461 is the square root of 212 521.
Number of digits of 461
461 is a number with 3 digits.
What are the multiples of 461?
The multiples of 461 are all integers evenly divisible by 461, that is all numbers such that the remainder of the division by 461 is zero. There are infinitely many multiples of 461. The smallest multiples of 461 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 461 too, since 0 × 461 = 0
- 461: indeed, 461 is a multiple of itself, since 461 is evenly divisible by 461 (we have 461 / 461 = 1, so the remainder of this division is indeed zero)
- 922: indeed, 922 = 461 × 2
- 1 383: indeed, 1 383 = 461 × 3
- 1 844: indeed, 1 844 = 461 × 4
- 2 305: indeed, 2 305 = 461 × 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 461). 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 21.471). 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.