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Find the H.C.F. of 3,6,9.

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Last updated date: 14th Jul 2024
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Answer
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Hint: In this type of question we have to use the concept factorisation. We know that the H.C.F. of given numbers is the greatest number which divides all the numbers without leaving a remainder. We have to first find prime factorisation of each of the numbers then we select common factors for all of them. Lastly, to find the H.C.F. of the given numbers perform multiplication of the common factors.

Complete step by step answer:
Now, here we have to find the H.C.F. of 3, 6, and 9.
We have to perform prime factorisation of each of the given numbers. In other words, factorise each number.
So that we can write,
\[\begin{align}
  & \Rightarrow 3=1\times 3 \\
 & \Rightarrow 6=1\times 2\times 3 \\
 & \Rightarrow 9=1\times 3\times 3 \\
\end{align}\]
Hence, the common factors are \[\left\{ 1,3 \right\}\].
Now, we will take these factors and performing multiplication to obtain H.C.F., as follows:
\[\text{H}\text{.C}\text{.F = }1\times 3=3\]
Therefore, the highest common factor of 3, 6 and 9 is 3.
Thus, the H.C.F. of 3, 6 and 9 is 3.

Note: In this type of question students have to note that the best way to find the H.C.F. is first find prime factorisation of all the given numbers and then find the product of the common factors. Students have to remember that they must multiply all the common factors only once to get the H.C.F. One of the students may solve as follows:
Step I – We have to find all the factors of 3, 6 and 9.
\[\begin{align}
  & \Rightarrow \text{Factors of 3 = }\left\{ 1,3 \right\} \\
 & \Rightarrow \text{Factors of 6 = }\left\{ 1,2,3 \right\} \\
 & \Rightarrow \text{Factors of 9 = }\left\{ 1,3,3 \right\} \\
\end{align}\]
Step II – Now we will find all the common factors
\[\Rightarrow \text{Common Factors of 3, 6 and 9 = }\left\{ 1,3 \right\}\]
Step III – Finally we have to select the highest common factor from the above common factors.
\[\Rightarrow \text{Highest Common Factor of 3, 6 and 9 = 3}\]
Thus, the H.C.F. of 3, 6 and 9 is 3.