It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 971, the answer is: yes, 971 is a prime number because it has only two distinct divisors: 1 and itself (971).
As a consequence, 971 is only a multiple of 1 and 971..
Since 971 is a prime number, 971 is also a deficient number, that is to say 971 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 971 without 971 itself (that is 1, by definition!).
Parity of 971
971 is an odd number, because it is not evenly divisible by 2.
Is 971 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 971 is about 31.161.
Thus, the square root of 971 is not an integer, and therefore 971 is not a square number.
Anyway, 971 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 971?
The square of a number (here 971) is the result of the product of this number (971) by itself (i.e., 971 × 971); the square of 971 is sometimes called "raising 971 to the power 2", or "971 squared".
As a consequence, 971 is the square root of 942 841.
Number of digits of 971
971 is a number with 3 digits.
What are the multiples of 971?
The multiples of 971 are all integers evenly divisible by 971, that is all numbers such that the remainder of the division by 971 is zero. There are infinitely many multiples of 971. The smallest multiples of 971 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 971 too, since 0 × 971 = 0
- 971: indeed, 971 is a multiple of itself, since 971 is evenly divisible by 971 (we have 971 / 971 = 1, so the remainder of this division is indeed zero)
- 1 942: indeed, 1 942 = 971 × 2
- 2 913: indeed, 2 913 = 971 × 3
- 3 884: indeed, 3 884 = 971 × 4
- 4 855: indeed, 4 855 = 971 × 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 971). 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 31.161). 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.