Question

The HCF of any two prime numbers \[a\] and \[b\] is
A.\[a\]
B.\[ab\]
C.\[b\]
D.\[1\]

Answer 1

Hint: In the given question, we have been given that there are two numbers \[a\] and \[b\] which are prime. We have to find their HCF. This question can be easily solved if we know what prime numbers are, what an HCF of two numbers is and then we correlate them and we are going to get our answer.

Complete step-by-step answer:
The HCF (Highest Common Factor) of any two numbers is the biggest number which divides both of the numbers.
A prime number is a number which has only two factors – \[1\] and the number itself.
Now, since \[a\] and \[b\] are both primes, they can be written as:
\[a = 1 \times a\]
and, \[b = 1 \times b\]
Now, in both of the numbers, there is only one common factor, which is \[1\].
Hence, we can say that the HCF of any two prime numbers \[a\] and \[b\] is \[1\].
Thus, the correct option is D.

Note: So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we think about the concept or formula which contains the known and the unknown and pick the one which is the most suitable and the most effective for finding the answer of the given question. Then we use the results or finding of the concept and apply it to our question. It is really important to know and follow all the results of the concepts if we have to solve the question correctly, as one slightest error gives the incorrect result.