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?

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.

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).