Question

Find the HCF of two co - prime numbers.

Answer 1

Hint: First, write the definitions of both HCF or Highest common factor and co – prime numbers. Apply the definition of Highest common factor to the definition of co – prime numbers to arrive at the final answer.

Complete step-by-step answer:
In this question, we need to find the HCF or Highest Common Factor of two co – prime numbers.

Let us first define what co – prime numbers actually are.

In number theory, two integers a and b are said to be relatively prime, mutually prime, or co - prime if the only positive integer (factor) that divides both of them is 1. Consequently, any prime number that divides one does not divide the other.

Now, let us define what HCF of the Highest Common Factor is.

In mathematics, the highest common factor also known as the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

Now, from the definition of co – prime numbers, we see that out of all the factors of two integers, a and b which are co- prime, the only positive integer (factor) that divides both of them is 1, i.e. any prime number that divides one does not divide the other.

This means that 1 is the only common factor of the two co – prime numbers and is consequently their highest common factor.

From the above statements, we come to the conclusion that the HCF of two co – prime numbers is equal to 1.

Note: In this question, it is very important to understand what HCF or Highest Common Factor actually is. Then you have to use this definition along with the definition of co – prime numbers to find the final answer. For example, 2 and 3 are coprimes.