Question & Answer
QUESTION

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

ANSWER Verified Verified
Hint: First of all we will have to know about HCF. HCF is the largest or greatest factor common to any two or more given natural numbers.

Complete step-by-step answer:

We have been given that \[4=2\times 2\text{ and 15=3}\times \text{5}\],
Since there is no common prime factor , so HCF of 4 and 15 is 0.

But this is not the correct answer which means HCF of 4 and 15 is not equal to zero, it is equal to 1 given as follows:
$\begin{align}
  & \text{factor of 4=2}\times 2\times 1 \\
 & \text{factor of 15=}3\times 5\times 1 \\
\end{align}$

Clearly, we can see that the highest common factor is 1.
\[\therefore \] HCF = 1 is the correct HCF.

Note: The two integers a and b are said to be co-prime numbers if the only positive integer (factor) that divides both of them is 1. A set of integers can also be called coprime if its elements share no common positive factor except 1.
Co-prime number is also known as relatively prime number or mutually prime number.
The HCF of two co-prime numbers are always equal to 1.
HCF is also known as the greatest common divisor (GCD).