It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 997, the answer is: yes, 997 is a prime number because it has only two distinct divisors: 1 and itself (997).
As a consequence, 997 is only a multiple of 1 and 997..
Since 997 is a prime number, 997 is also a deficient number, that is to say 997 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 997 without 997 itself (that is 1, by definition!).
Parity of 997
997 is an odd number, because it is not evenly divisible by 2.
Is 997 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 997 is about 31.575.
Thus, the square root of 997 is not an integer, and therefore 997 is not a square number.
Anyway, 997 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 997?
The square of a number (here 997) is the result of the product of this number (997) by itself (i.e., 997 × 997); the square of 997 is sometimes called "raising 997 to the power 2", or "997 squared".
As a consequence, 997 is the square root of 994 009.
Number of digits of 997
997 is a number with 3 digits.
What are the multiples of 997?
The multiples of 997 are all integers evenly divisible by 997, that is all numbers such that the remainder of the division by 997 is zero. There are infinitely many multiples of 997. The smallest multiples of 997 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 997 too, since 0 × 997 = 0
- 997: indeed, 997 is a multiple of itself, since 997 is evenly divisible by 997 (we have 997 / 997 = 1, so the remainder of this division is indeed zero)
- 1 994: indeed, 1 994 = 997 × 2
- 2 991: indeed, 2 991 = 997 × 3
- 3 988: indeed, 3 988 = 997 × 4
- 4 985: indeed, 4 985 = 997 × 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 997). 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 31.575). 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.