Question

The HCF of any two prime numbers $a{\text{ and }}b$ is:
A. $a$
B. $ab$
C. $b$
D. $1$

Answer 1

Hint: The HCF of any two prime numbers will be $1$ as there will be only one factor common which is $1$ in any two prime numbers.

Complete step-by-step answer:
Here we are given to find the HCF of any two numbers $a{\text{ and }}b$ which are said to be prime. So we must firstly know what we mean by the prime numbers. Prime numbers are the numbers that have only two factors which are $1$ and the number itself. For example: If we have the number $2$ we can write it as $2 = 2 \times 1$ so we get that $2$ has two factors which are $1{\text{ and 2}}$ itself. So it is a prime number.
Now one more example will make it clearer. Here we have the number $4$ and we need to find the factors of this number. So we can write it as:
$
  4 = 1 \times 4 \\
  4 = 2 \times 2 \\
 $
So we get that it has more than two factors which are $1,2,4$ and hence it is not a prime number.
Now we need to find the HCF of any number. We need to find the factor that is the highest of all the factors that is common to both the numbers.
So if we see the two prime numbers. Then both of them will have the common factor that is $1$ and other two numbers are different which are $a{\text{ and }}b$
So we can say that as $a{\text{ and }}b$ can be written as:
$
  a = a \times 1 \\
  b = b \times 1 \\
 $
So we can see that the common factor is only one.
Hence HCF of any two prime numbers is $1$
So D is the correct option.

Note: Here if we were asked to find the LCM of the two prime numbers $a{\text{ and }}b$ then it will be $ab$