Answer
Verified
375.9k+ views
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.
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.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE