Question

The HCF of two or more prime numbers is always _____.

Answer 1

Hint: A prime number is a natural number (counting number = 1,2,3,4,5,……….) greater than $1$ that is not a product of two smaller natural numbers or a number which has only two factors $1$ and the number itself is termed as a prime number. HCF is the highest common factor. It means the greatest number which divides two or more numbers is termed as H.C.F of them. The highest common factor (HCF) of two numbers $x$ and $y$ is the highest possible number that divides the numbers $x$ and $y$ exactly, leaving the remainder $0$.

Complete step-by-step solution:
Consider two prime numbers $x$ and $y$. The only divisors of $x$ are $1$ and $x$. Similarly, for $y$ its only divisors are $1$ and $y$. Since $x$ and $y$ both are different prime numbers, they have no common factor other than $1$. So, the highest common factor or HCF of $x$ and $y$ is $1$.
Let us take an example:
Let us take two prime numbers: $5$ and $37$.
Now, we will find the H.C.F of these prime numbers.
Find factors of $5$ and $37$.
The factors of $5$ are: $1,5$
The factors of $37$ are: $1,37$
Since $1$ is the only common factor of $5$ and $37$, it follows that the highest common factor or HCF of $5$ and $37$is $1$.

Note: Use the definitions and concepts to understand the terms. Don’t get confused between H.C.F and L.C.M as H.C.F is the highest common factor of two or more numbers whereas L.C.M is the lowest common multiple of two or more numbers.