Answer
Verified
446.7k+ views
Hint: First of all, we should write all factors 2, 3 and 5. Now we should consider the common factors of 2, 3 and 5. Among the factors of 2, 3 and 5, we have to find the highest common factor of 2, 3 and 5. The highest common factor of 2, 3 and 5 gives the H.C.F of 2, 3 and 5. In this way, we can find the H.C.F of 2, 3 and 5.
Complete step-by-step answer:
Before solving the question, we should understand the concept of H.C.F. To find H.C.F of three numbers, we should mention each and every factor of three numbers. Now we have to write all the common factors of three numbers. Among the common factors, we have to find the highest common factor. This highest common factor is called H.C.F.
In the question, we are given three numbers 2,3 and 5. Now we have to find the H.C.F of 2,3,5.
\[\begin{align}
& 2=2\times 1....(1) \\
& 3=3\times 1....(2) \\
& 5=5\times 1....(3) \\
\end{align}\]
From equation (1), equation (2) and equation (3), we are having the factors of 2, 3 and 5.
The common factor of 2, 3 and 5 is 1.
So, the H.C.F of 2, 3 and 5 is equal to 1.
Note: This problem can be solved in an alternative method also.
We know that the product of n numbers is equal to H.C.F of n numbers and L.C.M of n numbers.
From the question, we are given to find the H.C.F of 2,3 and 5.
The product of 2,3 and 5 \[=2\times 3\times 5=30\]
Now have to find the L.C.M of 2,3 and 5.
The multiples of 2 are 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36, …
The multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36, 39, ……
The multiples of 5 are 5,10,15,20,25,30,35,40,45, 50, …….
The common multiples of 2,3 and 5 are 30, 60, 90, ….
The least common multiple of 2,3 and 5 is 30.
So, the L.C.M of 2,3 and 5 is equal to 30.
We know that the product of 2,3 and 5 is equal to H.C.F of 2,3 and 5 and L.C.M of 2,3 and 5.
\[\begin{align}
& \Rightarrow 30=30\times \text{H}\text{.C}\text{.F} \\
& \Rightarrow \text{H}\text{.C}\text{.F=1} \\
\end{align}\]
So, the H.C.F of 2, 3 and 5 is equal 1.
Complete step-by-step answer:
Before solving the question, we should understand the concept of H.C.F. To find H.C.F of three numbers, we should mention each and every factor of three numbers. Now we have to write all the common factors of three numbers. Among the common factors, we have to find the highest common factor. This highest common factor is called H.C.F.
In the question, we are given three numbers 2,3 and 5. Now we have to find the H.C.F of 2,3,5.
\[\begin{align}
& 2=2\times 1....(1) \\
& 3=3\times 1....(2) \\
& 5=5\times 1....(3) \\
\end{align}\]
From equation (1), equation (2) and equation (3), we are having the factors of 2, 3 and 5.
The common factor of 2, 3 and 5 is 1.
So, the H.C.F of 2, 3 and 5 is equal to 1.
Note: This problem can be solved in an alternative method also.
We know that the product of n numbers is equal to H.C.F of n numbers and L.C.M of n numbers.
From the question, we are given to find the H.C.F of 2,3 and 5.
The product of 2,3 and 5 \[=2\times 3\times 5=30\]
Now have to find the L.C.M of 2,3 and 5.
The multiples of 2 are 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36, …
The multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36, 39, ……
The multiples of 5 are 5,10,15,20,25,30,35,40,45, 50, …….
The common multiples of 2,3 and 5 are 30, 60, 90, ….
The least common multiple of 2,3 and 5 is 30.
So, the L.C.M of 2,3 and 5 is equal to 30.
We know that the product of 2,3 and 5 is equal to H.C.F of 2,3 and 5 and L.C.M of 2,3 and 5.
\[\begin{align}
& \Rightarrow 30=30\times \text{H}\text{.C}\text{.F} \\
& \Rightarrow \text{H}\text{.C}\text{.F=1} \\
\end{align}\]
So, the H.C.F of 2, 3 and 5 is equal 1.
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
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
10 examples of evaporation in daily life with explanations
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Why is there a time difference of about 5 hours between class 10 social science CBSE