It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 719, the answer is: yes, 719 is a prime number because it has only two distinct divisors: 1 and itself (719).
As a consequence, 719 is only a multiple of 1 and 719..
Since 719 is a prime number, 719 is also a deficient number, that is to say 719 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 719 without 719 itself (that is 1, by definition!).
Parity of 719
719 is an odd number, because it is not evenly divisible by 2.
Is 719 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 719 is about 26.814.
Thus, the square root of 719 is not an integer, and therefore 719 is not a square number.
Anyway, 719 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 719?
The square of a number (here 719) is the result of the product of this number (719) by itself (i.e., 719 × 719); the square of 719 is sometimes called "raising 719 to the power 2", or "719 squared".
As a consequence, 719 is the square root of 516 961.
Number of digits of 719
719 is a number with 3 digits.
What are the multiples of 719?
The multiples of 719 are all integers evenly divisible by 719, that is all numbers such that the remainder of the division by 719 is zero. There are infinitely many multiples of 719. The smallest multiples of 719 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 719 too, since 0 × 719 = 0
- 719: indeed, 719 is a multiple of itself, since 719 is evenly divisible by 719 (we have 719 / 719 = 1, so the remainder of this division is indeed zero)
- 1 438: indeed, 1 438 = 719 × 2
- 2 157: indeed, 2 157 = 719 × 3
- 2 876: indeed, 2 876 = 719 × 4
- 3 595: indeed, 3 595 = 719 × 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 719). 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 26.814). 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.