It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 307, the answer is: yes, 307 is a prime number because it has only two distinct divisors: 1 and itself (307).
As a consequence, 307 is only a multiple of 1 and 307..
Since 307 is a prime number, 307 is also a deficient number, that is to say 307 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 307 without 307 itself (that is 1, by definition!).
Parity of 307
307 is an odd number, because it is not evenly divisible by 2.
Is 307 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 307 is about 17.521.
Thus, the square root of 307 is not an integer, and therefore 307 is not a square number.
Anyway, 307 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 307?
The square of a number (here 307) is the result of the product of this number (307) by itself (i.e., 307 × 307); the square of 307 is sometimes called "raising 307 to the power 2", or "307 squared".
As a consequence, 307 is the square root of 94 249.
Number of digits of 307
307 is a number with 3 digits.
What are the multiples of 307?
The multiples of 307 are all integers evenly divisible by 307, that is all numbers such that the remainder of the division by 307 is zero. There are infinitely many multiples of 307. The smallest multiples of 307 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 307 too, since 0 × 307 = 0
- 307: indeed, 307 is a multiple of itself, since 307 is evenly divisible by 307 (we have 307 / 307 = 1, so the remainder of this division is indeed zero)
- 614: indeed, 614 = 307 × 2
- 921: indeed, 921 = 307 × 3
- 1 228: indeed, 1 228 = 307 × 4
- 1 535: indeed, 1 535 = 307 × 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 307). 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 17.521). 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.