It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 709, the answer is: yes, 709 is a prime number because it has only two distinct divisors: 1 and itself (709).
As a consequence, 709 is only a multiple of 1 and 709..
Since 709 is a prime number, 709 is also a deficient number, that is to say 709 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 709 without 709 itself (that is 1, by definition!).
Parity of 709
709 is an odd number, because it is not evenly divisible by 2.
Is 709 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 709 is about 26.627.
Thus, the square root of 709 is not an integer, and therefore 709 is not a square number.
Anyway, 709 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 709?
The square of a number (here 709) is the result of the product of this number (709) by itself (i.e., 709 × 709); the square of 709 is sometimes called "raising 709 to the power 2", or "709 squared".
As a consequence, 709 is the square root of 502 681.
Number of digits of 709
709 is a number with 3 digits.
What are the multiples of 709?
The multiples of 709 are all integers evenly divisible by 709, that is all numbers such that the remainder of the division by 709 is zero. There are infinitely many multiples of 709. The smallest multiples of 709 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 709 too, since 0 × 709 = 0
- 709: indeed, 709 is a multiple of itself, since 709 is evenly divisible by 709 (we have 709 / 709 = 1, so the remainder of this division is indeed zero)
- 1 418: indeed, 1 418 = 709 × 2
- 2 127: indeed, 2 127 = 709 × 3
- 2 836: indeed, 2 836 = 709 × 4
- 3 545: indeed, 3 545 = 709 × 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 709). 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 26.627). 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.