It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 359, the answer is: yes, 359 is a prime number because it has only two distinct divisors: 1 and itself (359).
As a consequence, 359 is only a multiple of 1 and 359..
Since 359 is a prime number, 359 is also a deficient number, that is to say 359 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 359 without 359 itself (that is 1, by definition!).
Parity of 359
359 is an odd number, because it is not evenly divisible by 2.
Is 359 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 359 is about 18.947.
Thus, the square root of 359 is not an integer, and therefore 359 is not a square number.
Anyway, 359 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 359?
The square of a number (here 359) is the result of the product of this number (359) by itself (i.e., 359 × 359); the square of 359 is sometimes called "raising 359 to the power 2", or "359 squared".
As a consequence, 359 is the square root of 128 881.
Number of digits of 359
359 is a number with 3 digits.
What are the multiples of 359?
The multiples of 359 are all integers evenly divisible by 359, that is all numbers such that the remainder of the division by 359 is zero. There are infinitely many multiples of 359. The smallest multiples of 359 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 359 too, since 0 × 359 = 0
- 359: indeed, 359 is a multiple of itself, since 359 is evenly divisible by 359 (we have 359 / 359 = 1, so the remainder of this division is indeed zero)
- 718: indeed, 718 = 359 × 2
- 1 077: indeed, 1 077 = 359 × 3
- 1 436: indeed, 1 436 = 359 × 4
- 1 795: indeed, 1 795 = 359 × 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 359). 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 18.947). 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.