Is 47 a prime number or composite? This question often arises when discussing the fundamentals of number theory. In order to determine whether 47 is a prime or composite number, we need to understand the definitions of these two types of numbers and apply them to the given value.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. This means that a prime number cannot be formed by multiplying two smaller natural numbers. On the other hand, a composite number is a natural number greater than 1 that can be formed by multiplying two smaller natural numbers.
To determine if 47 is a prime number, we need to check if it has any divisors other than 1 and itself. One way to do this is by dividing 47 by all the natural numbers less than 47 and checking if any of them divide 47 without leaving a remainder. However, this process can be time-consuming and inefficient.
A more efficient approach is to use the fact that if a number is divisible by any prime number, then it must be divisible by a prime number less than or equal to its square root. This is because if a number is divisible by a prime number greater than its square root, then it must also be divisible by a prime number less than or equal to its square root.
Since 47 is less than 64 (which is 8 squared), we only need to check for divisors up to the square root of 47, which is approximately 6.855. By checking for divisors in this range, we can determine if 47 is a prime number or composite.
Upon checking, we find that 47 is not divisible by any prime number less than or equal to its square root. Therefore, we can conclude that 47 is a prime number. This means that 47 cannot be formed by multiplying two smaller natural numbers and has no positive divisors other than 1 and itself.
In summary, the answer to the question “Is 47 a prime number or composite?” is that 47 is a prime number. This conclusion is based on the efficient method of checking for divisors up to the square root of the given number and the fact that 47 has no divisors other than 1 and itself.
