Question & Answer
QUESTION

HCF of co-prime numbers 4 and 15 was found as follows by factorisation: $4=2\times 2$ and $15=3\times 5$ . Since there is no common prime factor, HCF of 4 and 15 is 0. Is this answer correct? If not, what is the correct HCF?

ANSWER Verified Verified
Hint: For solving this question we should know how to find the HCF of any two numbers and then the basic definition of co-prime numbers will be required to answer correctly.

Complete step-by-step answer:

Given:
Two numbers 4 and 15.
And it is given that there HCF is 0.
Firstly, we should know that we can not divide any number by 0. So, we can say that 0 cannot be the factor of both 4 and 15. Then, the HCF of 4 and 5 given in the question is a wrong answer.

Now, we have to find the HCF of 4 and 15. For which firstly we find factors of 4 and 15 separately and then we will easily find the highest common factor (HCF) for them.

Factors of 4:
We can write, $4=1\times 2\times 2$ . Then,
Factors of 4 will be 1, 2, and 4.

Factors of 15:
We can write, $15=1\times 3\times 5$ . Then,
Factors of 15 will be 1, 3, 5 and 15.

Now, as we have determined the factors of 4 and 15. So, we can find the HCF of 4 and 15 very easily. We have:
Factors of $4=\left\{ 1,2,4 \right\}$ .
Factors of $15=\left\{ 1,3,5,15 \right\}$ .

From the above two equations, we can figure out that among all factors of 4 and 15 there is only one common factor and that is 1. So, 1 will be the HCF of 4 and 15.
Now, we can define the definition of co-prime numbers as any two positive integers whose HCF is 1 are said to be coprime relative to each other.

Note: Here, students should know how to find the factors and a very important point to note here is that we should not confuse the 0 given in the question as HCF. And we should not confuse between coprime and prime numbers while solving this question.