It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 367, the answer is: yes, 367 is a prime number because it has only two distinct divisors: 1 and itself (367).
As a consequence, 367 is only a multiple of 1 and 367..
Since 367 is a prime number, 367 is also a deficient number, that is to say 367 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 367 without 367 itself (that is 1, by definition!).
Parity of 367
367 is an odd number, because it is not evenly divisible by 2.
Is 367 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 367 is about 19.157.
Thus, the square root of 367 is not an integer, and therefore 367 is not a square number.
Anyway, 367 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 367?
The square of a number (here 367) is the result of the product of this number (367) by itself (i.e., 367 × 367); the square of 367 is sometimes called "raising 367 to the power 2", or "367 squared".
As a consequence, 367 is the square root of 134 689.
Number of digits of 367
367 is a number with 3 digits.
What are the multiples of 367?
The multiples of 367 are all integers evenly divisible by 367, that is all numbers such that the remainder of the division by 367 is zero. There are infinitely many multiples of 367. The smallest multiples of 367 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 367 too, since 0 × 367 = 0
- 367: indeed, 367 is a multiple of itself, since 367 is evenly divisible by 367 (we have 367 / 367 = 1, so the remainder of this division is indeed zero)
- 734: indeed, 734 = 367 × 2
- 1 101: indeed, 1 101 = 367 × 3
- 1 468: indeed, 1 468 = 367 × 4
- 1 835: indeed, 1 835 = 367 × 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 367). 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 19.157). 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.