It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 383, the answer is: yes, 383 is a prime number because it has only two distinct divisors: 1 and itself (383).
As a consequence, 383 is only a multiple of 1 and 383..
Since 383 is a prime number, 383 is also a deficient number, that is to say 383 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 383 without 383 itself (that is 1, by definition!).
Parity of 383
383 is an odd number, because it is not evenly divisible by 2.
Is 383 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 383 is about 19.570.
Thus, the square root of 383 is not an integer, and therefore 383 is not a square number.
Anyway, 383 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 383?
The square of a number (here 383) is the result of the product of this number (383) by itself (i.e., 383 × 383); the square of 383 is sometimes called "raising 383 to the power 2", or "383 squared".
As a consequence, 383 is the square root of 146 689.
Number of digits of 383
383 is a number with 3 digits.
What are the multiples of 383?
The multiples of 383 are all integers evenly divisible by 383, that is all numbers such that the remainder of the division by 383 is zero. There are infinitely many multiples of 383. The smallest multiples of 383 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 383 too, since 0 × 383 = 0
- 383: indeed, 383 is a multiple of itself, since 383 is evenly divisible by 383 (we have 383 / 383 = 1, so the remainder of this division is indeed zero)
- 766: indeed, 766 = 383 × 2
- 1 149: indeed, 1 149 = 383 × 3
- 1 532: indeed, 1 532 = 383 × 4
- 1 915: indeed, 1 915 = 383 × 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 383). 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 19.570). 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.