It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 347, the answer is: yes, 347 is a prime number because it has only two distinct divisors: 1 and itself (347).
As a consequence, 347 is only a multiple of 1 and 347..
Since 347 is a prime number, 347 is also a deficient number, that is to say 347 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 347 without 347 itself (that is 1, by definition!).
Parity of 347
347 is an odd number, because it is not evenly divisible by 2.
Is 347 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 347 is about 18.628.
Thus, the square root of 347 is not an integer, and therefore 347 is not a square number.
Anyway, 347 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 347?
The square of a number (here 347) is the result of the product of this number (347) by itself (i.e., 347 × 347); the square of 347 is sometimes called "raising 347 to the power 2", or "347 squared".
As a consequence, 347 is the square root of 120 409.
Number of digits of 347
347 is a number with 3 digits.
What are the multiples of 347?
The multiples of 347 are all integers evenly divisible by 347, that is all numbers such that the remainder of the division by 347 is zero. There are infinitely many multiples of 347. The smallest multiples of 347 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 347 too, since 0 × 347 = 0
- 347: indeed, 347 is a multiple of itself, since 347 is evenly divisible by 347 (we have 347 / 347 = 1, so the remainder of this division is indeed zero)
- 694: indeed, 694 = 347 × 2
- 1 041: indeed, 1 041 = 347 × 3
- 1 388: indeed, 1 388 = 347 × 4
- 1 735: indeed, 1 735 = 347 × 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 347). 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 18.628). 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.