Question

Write true or false. \[1\] is the smallest prime number?

Answer 1

Hint: Prime number is a number greater than \[1\] that number is not a product of two smaller natural numbers. prime numbers are part of whole numbers. prime numbers have two factors \[1\] and themselves.

Complete step-by-step solution:
 From the question we were given a statement “\[1\] is the smallest prime number” and we have to write whether this statement is true or false.
From the basic concepts of mathematics, we can say that a prime number is a natural number greater than \[1\] and that number cannot be written as a product of two smaller numbers. the prime number has only two factors \[1\] and itself.
Natural number greater than \[1\] and not a prime number is called a composite number.
Prime numbers have only two positive factors. Now for \[1\] the number of positive divisors or factors is only one i.e, \[1\] itself.
Prime number should be greater than 1. We know that \[1\] is always equal to \[1\]and never greater than \[1\]. It has overruled the definition of prime number. So, \[1\] cannot be a prime number.
\[1\] is neither a prime number nor a composite number.
According to the definition of prime number \[2\] is the smallest prime number as it satisfies all the conditions required for prime numbers. Now we can conclude that \[1\] is not a prime number.
”\[1\] is the smallest prime number” Is a false statement.

Note: This question is completely based upon concepts. Students should know the basic requirements required for a number to be a prime number. Many students may have the misconception that \[1\] is a prime number but actually \[1\] is neither a prime number nor a composite number.