It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 149, the answer is: yes, 149 is a prime number because it has only two distinct divisors: 1 and itself (149).
As a consequence, 149 is only a multiple of 1 and 149..
Since 149 is a prime number, 149 is also a deficient number, that is to say 149 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 149 without 149 itself (that is 1, by definition!).
Parity of 149
149 is an odd number, because it is not evenly divisible by 2.
Is 149 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 149 is about 12.207.
Thus, the square root of 149 is not an integer, and therefore 149 is not a square number.
Anyway, 149 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 149?
The square of a number (here 149) is the result of the product of this number (149) by itself (i.e., 149 × 149); the square of 149 is sometimes called "raising 149 to the power 2", or "149 squared".
As a consequence, 149 is the square root of 22 201.
Number of digits of 149
149 is a number with 3 digits.
What are the multiples of 149?
The multiples of 149 are all integers evenly divisible by 149, that is all numbers such that the remainder of the division by 149 is zero. There are infinitely many multiples of 149. The smallest multiples of 149 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 149 too, since 0 × 149 = 0
- 149: indeed, 149 is a multiple of itself, since 149 is evenly divisible by 149 (we have 149 / 149 = 1, so the remainder of this division is indeed zero)
- 298: indeed, 298 = 149 × 2
- 447: indeed, 447 = 149 × 3
- 596: indeed, 596 = 149 × 4
- 745: indeed, 745 = 149 × 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 149). 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 12.207). 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.