Question

How do you find HCF?

Answer 1

Step 1: Define the method of finding HCF

1. HCF stands for the highest common factor.
2. The product of all the common factors of two or more numbers is called the HCF of these numbers.
3. To find the HCF of any two numbers, first, find their prime factors by the prime factorization method.
4. Select only those prime factors which are common in both.
5. The product of these common factors is the required HCF.

Step 2: Give an example

Let us take an example to understand the process of finding HCF.

Let, $6$ and $15$ are two numbers whose HCF has to be calculated.

Now, by prime factorisation of $6$ and $15$, we have,

$\begin{array}{cc}2& 6\\ 3& 3\\ & 1\end{array}\begin{array}{cc}3& 15\\ 5& 5\\ & 1\end{array}$

So, $6=2\times 3\times 1$

And, $15=3\times 5\times 1$

Thus, $\mathrm{HCF}\left(6,15\right)=$ common factors of $6$ and $15$

$\Rightarrow$ $\mathrm{HCF}\left(6,15\right)=3\times 1$

$\Rightarrow$ $\mathrm{HCF}\left(6,15\right)=3$

Hence, the HCF of two or more numbers can be calculated by multiplying the common prime factors of the given numbers.