It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 7, the answer is: yes, 7 is a prime number because it has only two distinct divisors: 1 and itself (7).
As a consequence, 7 is only a multiple of 1 and 7..
Since 7 is a prime number, 7 is also a deficient number, that is to say 7 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 7 without 7 itself (that is 1, by definition!).
Parity of 7
7 is an odd number, because it is not evenly divisible by 2.
Is 7 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 7 is about 2.646.
Thus, the square root of 7 is not an integer, and therefore 7 is not a square number.
Anyway, 7 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 7?
The square of a number (here 7) is the result of the product of this number (7) by itself (i.e., 7 × 7); the square of 7 is sometimes called "raising 7 to the power 2", or "7 squared".
As a consequence, 7 is the square root of 49.
Number of digits of 7
7 is a single-digit number, because it is strictly less than 10; 7 is in fact itself a digit.
What are the multiples of 7?
The multiples of 7 are all integers evenly divisible by 7, that is all numbers such that the remainder of the division by 7 is zero. There are infinitely many multiples of 7. The smallest multiples of 7 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 7 too, since 0 × 7 = 0
- 7: indeed, 7 is a multiple of itself, since 7 is evenly divisible by 7 (we have 7 / 7 = 1, so the remainder of this division is indeed zero)
- 14: indeed, 14 = 7 × 2
- 21: indeed, 21 = 7 × 3
- 28: indeed, 28 = 7 × 4
- 35: indeed, 35 = 7 × 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 7). 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 2.646). 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.