It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 317, the answer is: yes, 317 is a prime number because it has only two distinct divisors: 1 and itself (317).
As a consequence, 317 is only a multiple of 1 and 317..
Since 317 is a prime number, 317 is also a deficient number, that is to say 317 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 317 without 317 itself (that is 1, by definition!).
Parity of 317
317 is an odd number, because it is not evenly divisible by 2.
Is 317 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 317 is about 17.804.
Thus, the square root of 317 is not an integer, and therefore 317 is not a square number.
Anyway, 317 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 317?
The square of a number (here 317) is the result of the product of this number (317) by itself (i.e., 317 × 317); the square of 317 is sometimes called "raising 317 to the power 2", or "317 squared".
As a consequence, 317 is the square root of 100 489.
Number of digits of 317
317 is a number with 3 digits.
What are the multiples of 317?
The multiples of 317 are all integers evenly divisible by 317, that is all numbers such that the remainder of the division by 317 is zero. There are infinitely many multiples of 317. The smallest multiples of 317 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 317 too, since 0 × 317 = 0
- 317: indeed, 317 is a multiple of itself, since 317 is evenly divisible by 317 (we have 317 / 317 = 1, so the remainder of this division is indeed zero)
- 634: indeed, 634 = 317 × 2
- 951: indeed, 951 = 317 × 3
- 1 268: indeed, 1 268 = 317 × 4
- 1 585: indeed, 1 585 = 317 × 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 317). 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 17.804). 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.