It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 181, the answer is: yes, 181 is a prime number because it has only two distinct divisors: 1 and itself (181).
As a consequence, 181 is only a multiple of 1 and 181..
Since 181 is a prime number, 181 is also a deficient number, that is to say 181 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 181 without 181 itself (that is 1, by definition!).
Parity of 181
181 is an odd number, because it is not evenly divisible by 2.
Is 181 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 181 is about 13.454.
Thus, the square root of 181 is not an integer, and therefore 181 is not a square number.
Anyway, 181 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 181?
The square of a number (here 181) is the result of the product of this number (181) by itself (i.e., 181 × 181); the square of 181 is sometimes called "raising 181 to the power 2", or "181 squared".
As a consequence, 181 is the square root of 32 761.
Number of digits of 181
181 is a number with 3 digits.
What are the multiples of 181?
The multiples of 181 are all integers evenly divisible by 181, that is all numbers such that the remainder of the division by 181 is zero. There are infinitely many multiples of 181. The smallest multiples of 181 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 181 too, since 0 × 181 = 0
- 181: indeed, 181 is a multiple of itself, since 181 is evenly divisible by 181 (we have 181 / 181 = 1, so the remainder of this division is indeed zero)
- 362: indeed, 362 = 181 × 2
- 543: indeed, 543 = 181 × 3
- 724: indeed, 724 = 181 × 4
- 905: indeed, 905 = 181 × 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 181). 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 13.454). 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.