It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 727, the answer is: yes, 727 is a prime number because it has only two distinct divisors: 1 and itself (727).
As a consequence, 727 is only a multiple of 1 and 727..
Since 727 is a prime number, 727 is also a deficient number, that is to say 727 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 727 without 727 itself (that is 1, by definition!).
Parity of 727
727 is an odd number, because it is not evenly divisible by 2.
Is 727 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 727 is about 26.963.
Thus, the square root of 727 is not an integer, and therefore 727 is not a square number.
Anyway, 727 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 727?
The square of a number (here 727) is the result of the product of this number (727) by itself (i.e., 727 × 727); the square of 727 is sometimes called "raising 727 to the power 2", or "727 squared".
As a consequence, 727 is the square root of 528 529.
Number of digits of 727
727 is a number with 3 digits.
What are the multiples of 727?
The multiples of 727 are all integers evenly divisible by 727, that is all numbers such that the remainder of the division by 727 is zero. There are infinitely many multiples of 727. The smallest multiples of 727 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 727 too, since 0 × 727 = 0
- 727: indeed, 727 is a multiple of itself, since 727 is evenly divisible by 727 (we have 727 / 727 = 1, so the remainder of this division is indeed zero)
- 1 454: indeed, 1 454 = 727 × 2
- 2 181: indeed, 2 181 = 727 × 3
- 2 908: indeed, 2 908 = 727 × 4
- 3 635: indeed, 3 635 = 727 × 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 727). 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 26.963). 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.