Question

Find the H.C.F of 7, 14, 3.

Answer 1

Hint: In this type of question we have to use the concept of H.C.F. When we try to find out the H.C.F. we have to first write all the factors of the given numbers. Then we should consider all common factors of the given numbers. Now from the common factors we have to find out the highest common factor. This highest common factor is nothing but the H.C.F of the given numbers. In this way we can find out the H.C.F of the given numbers.

Complete step by step answer:
Now, we have to find out the H.C.F of 7, 14 and 3.
Let us consider the all possible factors of 7, 14 and 3 which are as follows:
\[\begin{align}
  & \Rightarrow 7=7\times 1 \\
 & \Rightarrow 14=7\times 2\times 1 \\
 & \Rightarrow 3=3\times 1 \\
\end{align}\]
Now, we have to find out all the common factors of 7, 14 and 3.
Hence, we can observe that the common factor of 7, 14 and 3 is 1.
Thus, the highest common factor i.e. H.C.F. of 7, 14 and 3 is $1$.

Note: In this type of question students need to remember that the H.C.F has to be only one number. It is the highest possible common factor of all the given numbers. Also students have to take care while finding H.C.F of the numbers doesn’t mix up HCF with LCM. As H.C.F stands for highest common factors we first find out all the factors of the given numbers and then from the common factors we select the highest common factor as H.C.F. While in calculation of LCM first we list down all the multiples of the given numbers and then from the common multiples we select the least common multiple as LCM.