It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 353, the answer is: yes, 353 is a prime number because it has only two distinct divisors: 1 and itself (353).
As a consequence, 353 is only a multiple of 1 and 353..
Since 353 is a prime number, 353 is also a deficient number, that is to say 353 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 353 without 353 itself (that is 1, by definition!).
Parity of 353
353 is an odd number, because it is not evenly divisible by 2.
Is 353 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 353 is about 18.788.
Thus, the square root of 353 is not an integer, and therefore 353 is not a square number.
Anyway, 353 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 353?
The square of a number (here 353) is the result of the product of this number (353) by itself (i.e., 353 × 353); the square of 353 is sometimes called "raising 353 to the power 2", or "353 squared".
As a consequence, 353 is the square root of 124 609.
Number of digits of 353
353 is a number with 3 digits.
What are the multiples of 353?
The multiples of 353 are all integers evenly divisible by 353, that is all numbers such that the remainder of the division by 353 is zero. There are infinitely many multiples of 353. The smallest multiples of 353 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 353 too, since 0 × 353 = 0
- 353: indeed, 353 is a multiple of itself, since 353 is evenly divisible by 353 (we have 353 / 353 = 1, so the remainder of this division is indeed zero)
- 706: indeed, 706 = 353 × 2
- 1 059: indeed, 1 059 = 353 × 3
- 1 412: indeed, 1 412 = 353 × 4
- 1 765: indeed, 1 765 = 353 × 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 353). 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 18.788). 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.