Question

 What is the HCF of the smallest prime number and the smallest composite number?

Answer 1

Hint: For solving this question first we will see the definitions of prime numbers and composite numbers. After that, we will write the smallest prime number and the smallest composite number. Then, we will express them into multiples of the prime numbers only and ultimately find their HCF easily.
Complete step by step answer:
Given:
We have to find the HCF of the smallest prime number and the smallest composite number.
Now, before we proceed we should know the definition of a prime number and the composite numbers.
Prime Numbers:
A prime number is a positive integer having exactly two factors. If $p$ is a prime number, then it’s only factors are necessarily 1 and $p$ itself. Any number which does not follow this termed as composite numbers which means that they can be factored into other positive integers. First ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Moreover, we should note that 1 is not a prime number.
Composite Numbers:
The integers which can be generated by multiplying the two smallest positive integers contains at least one divisor other than number ‘1’ and itself is known as composite numbers. These numbers always have more than two factors. First ten composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16 and 18. Moreover, 0 is considered as neither prime nor composite number because it does not have any factors.
Now, form the above discussion we can say that 2 is the smallest prime number and 4 is the smallest composite number.
Now, first, we will write 2 and 4 into multiples of prime numbers only. Then,
$\begin{align}
  & 2=2 \\
 & 4=2\times 2 \\
\end{align}$
Now, from the above result, we can write that HCF of 2 and 4 will be 2.
Thus, 2 is the HCF of the smallest prime number and the smallest composite number.
Note: The question is very easy to solve but the student should know the definitions of prime numbers and composite numbers with clarity. And we should not miss any factor while writing the factors of the 2 and 4. Moreover, avoid making calculation mistakes while solving the question. After we have calculated the HCF, we should check whether it’s correct or not with simple arithmetic calculations.