It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 349, the answer is: yes, 349 is a prime number because it has only two distinct divisors: 1 and itself (349).
As a consequence, 349 is only a multiple of 1 and 349..
Since 349 is a prime number, 349 is also a deficient number, that is to say 349 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 349 without 349 itself (that is 1, by definition!).
Parity of 349
349 is an odd number, because it is not evenly divisible by 2.
Is 349 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 349 is about 18.682.
Thus, the square root of 349 is not an integer, and therefore 349 is not a square number.
Anyway, 349 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 349?
The square of a number (here 349) is the result of the product of this number (349) by itself (i.e., 349 × 349); the square of 349 is sometimes called "raising 349 to the power 2", or "349 squared".
As a consequence, 349 is the square root of 121 801.
Number of digits of 349
349 is a number with 3 digits.
What are the multiples of 349?
The multiples of 349 are all integers evenly divisible by 349, that is all numbers such that the remainder of the division by 349 is zero. There are infinitely many multiples of 349. The smallest multiples of 349 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 349 too, since 0 × 349 = 0
- 349: indeed, 349 is a multiple of itself, since 349 is evenly divisible by 349 (we have 349 / 349 = 1, so the remainder of this division is indeed zero)
- 698: indeed, 698 = 349 × 2
- 1 047: indeed, 1 047 = 349 × 3
- 1 396: indeed, 1 396 = 349 × 4
- 1 745: indeed, 1 745 = 349 × 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 349). 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 18.682). 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.