It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 127, the answer is: yes, 127 is a prime number because it has only two distinct divisors: 1 and itself (127).
As a consequence, 127 is only a multiple of 1 and 127..
Since 127 is a prime number, 127 is also a deficient number, that is to say 127 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 127 without 127 itself (that is 1, by definition!).
Parity of 127
127 is an odd number, because it is not evenly divisible by 2.
Is 127 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 127 is about 11.269.
Thus, the square root of 127 is not an integer, and therefore 127 is not a square number.
Anyway, 127 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 127?
The square of a number (here 127) is the result of the product of this number (127) by itself (i.e., 127 × 127); the square of 127 is sometimes called "raising 127 to the power 2", or "127 squared".
As a consequence, 127 is the square root of 16 129.
Number of digits of 127
127 is a number with 3 digits.
What are the multiples of 127?
The multiples of 127 are all integers evenly divisible by 127, that is all numbers such that the remainder of the division by 127 is zero. There are infinitely many multiples of 127. The smallest multiples of 127 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 127 too, since 0 × 127 = 0
- 127: indeed, 127 is a multiple of itself, since 127 is evenly divisible by 127 (we have 127 / 127 = 1, so the remainder of this division is indeed zero)
- 254: indeed, 254 = 127 × 2
- 381: indeed, 381 = 127 × 3
- 508: indeed, 508 = 127 × 4
- 635: indeed, 635 = 127 × 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 127). 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 11.269). 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.