It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 947, the answer is: yes, 947 is a prime number because it has only two distinct divisors: 1 and itself (947).
As a consequence, 947 is only a multiple of 1 and 947..
Since 947 is a prime number, 947 is also a deficient number, that is to say 947 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 947 without 947 itself (that is 1, by definition!).
Parity of 947
947 is an odd number, because it is not evenly divisible by 2.
Is 947 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 947 is about 30.773.
Thus, the square root of 947 is not an integer, and therefore 947 is not a square number.
Anyway, 947 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 947?
The square of a number (here 947) is the result of the product of this number (947) by itself (i.e., 947 × 947); the square of 947 is sometimes called "raising 947 to the power 2", or "947 squared".
As a consequence, 947 is the square root of 896 809.
Number of digits of 947
947 is a number with 3 digits.
What are the multiples of 947?
The multiples of 947 are all integers evenly divisible by 947, that is all numbers such that the remainder of the division by 947 is zero. There are infinitely many multiples of 947. The smallest multiples of 947 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 947 too, since 0 × 947 = 0
- 947: indeed, 947 is a multiple of itself, since 947 is evenly divisible by 947 (we have 947 / 947 = 1, so the remainder of this division is indeed zero)
- 1 894: indeed, 1 894 = 947 × 2
- 2 841: indeed, 2 841 = 947 × 3
- 3 788: indeed, 3 788 = 947 × 4
- 4 735: indeed, 4 735 = 947 × 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 947). 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 30.773). 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.