It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 739, the answer is: yes, 739 is a prime number because it has only two distinct divisors: 1 and itself (739).
As a consequence, 739 is only a multiple of 1 and 739..
Since 739 is a prime number, 739 is also a deficient number, that is to say 739 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 739 without 739 itself (that is 1, by definition!).
Parity of 739
739 is an odd number, because it is not evenly divisible by 2.
Is 739 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 739 is about 27.185.
Thus, the square root of 739 is not an integer, and therefore 739 is not a square number.
Anyway, 739 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 739?
The square of a number (here 739) is the result of the product of this number (739) by itself (i.e., 739 × 739); the square of 739 is sometimes called "raising 739 to the power 2", or "739 squared".
As a consequence, 739 is the square root of 546 121.
Number of digits of 739
739 is a number with 3 digits.
What are the multiples of 739?
The multiples of 739 are all integers evenly divisible by 739, that is all numbers such that the remainder of the division by 739 is zero. There are infinitely many multiples of 739. The smallest multiples of 739 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 739 too, since 0 × 739 = 0
- 739: indeed, 739 is a multiple of itself, since 739 is evenly divisible by 739 (we have 739 / 739 = 1, so the remainder of this division is indeed zero)
- 1 478: indeed, 1 478 = 739 × 2
- 2 217: indeed, 2 217 = 739 × 3
- 2 956: indeed, 2 956 = 739 × 4
- 3 695: indeed, 3 695 = 739 × 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 739). 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 27.185). 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.