Answer
Verified
455.1k+ views
Hint: We will first understand the concept of successive division method which is given as if a quotient of the dividend is taken and this is used as the dividend in the next division, such division is called “successive division”. We will solve this in two phases i.e. first we will find HCF of 567, 621. On getting an answer, we will find HCF of that answer, 675. On getting an answer to this, we will find the HCF of 567, 621, 675.
Complete step-by-step answer:
Here, we will first understand the concept of successive division method.
If a quotient of the dividend is taken and this is used as the dividend in the next division, such division is called “successive division”. This process can continue up to any number of steps until the quotient in the first division is taken and dividend in the second division; the quotient in the second division is taken as the dividend in the third division; the quotient in the third division is taken as the dividend in the fourth division and so on.
Now, we solve this in two phases. First, we will take 567, 621.
So, now we will divide 621 by 567. We get as
$ 567\overset{1}{\overline{\left){\begin{align}
& 621 \\
& 567 \\
& \overline{\text{ }54} \\
\end{align}}\right.}} $
Now, we will take divisor 567 as dividend and remainder 54 as divisor. On solving, we get as
$ 54\overset{10}{\overline{\left){\begin{align}
& 567 \\
& 540 \\
& \overline{\text{ 27}} \\
\end{align}}\right.}} $
Again, we will take divisor 54 as dividend and remainder as divisor. We will get as
$ 27\overset{2}{\overline{\left){\begin{align}
& 54 \\
& 54 \\
& \overline{\text{ 0}} \\
\end{align}}\right.}} $
Now, we got remainder 0 so, we will consider the divisor to be HCF of 567, 621 i.e. 27.
Now, we will find HCF of HCF $ \left( 567,621 \right) $ , 675 i.e. 27, 675.
Using the same concept done above, we will solve.
$ 27\overset{24}{\overline{\left){\begin{align}
& 675 \\
& 54\downarrow \\
& \overline{\text{135}} \\
& 132 \\
& \overline{\text{ }3} \\
\end{align}}\right.}} $
Now, we will take divisor 27 as dividend and remainder 3 to be divisor. We get as
$ 3\overset{9}{\overline{\left){\begin{align}
& 27 \\
& 27 \\
& \overline{\text{ }0} \\
\end{align}}\right.}} $
Thus, we can now say that divisor 3 is HCF of 567, 621, 675.
Thus, $ HCF\left( 567,621,675 \right) $ is 3.
Note: Do not assume a successive division method to be the same as normal division we do in prime factorization. Though the answer will be correct, the method of solving will be wrong. So, students should be clear with the methods of finding the highest common factor and then solve as per asked in question.
Complete step-by-step answer:
Here, we will first understand the concept of successive division method.
If a quotient of the dividend is taken and this is used as the dividend in the next division, such division is called “successive division”. This process can continue up to any number of steps until the quotient in the first division is taken and dividend in the second division; the quotient in the second division is taken as the dividend in the third division; the quotient in the third division is taken as the dividend in the fourth division and so on.
Now, we solve this in two phases. First, we will take 567, 621.
So, now we will divide 621 by 567. We get as
$ 567\overset{1}{\overline{\left){\begin{align}
& 621 \\
& 567 \\
& \overline{\text{ }54} \\
\end{align}}\right.}} $
Now, we will take divisor 567 as dividend and remainder 54 as divisor. On solving, we get as
$ 54\overset{10}{\overline{\left){\begin{align}
& 567 \\
& 540 \\
& \overline{\text{ 27}} \\
\end{align}}\right.}} $
Again, we will take divisor 54 as dividend and remainder as divisor. We will get as
$ 27\overset{2}{\overline{\left){\begin{align}
& 54 \\
& 54 \\
& \overline{\text{ 0}} \\
\end{align}}\right.}} $
Now, we got remainder 0 so, we will consider the divisor to be HCF of 567, 621 i.e. 27.
Now, we will find HCF of HCF $ \left( 567,621 \right) $ , 675 i.e. 27, 675.
Using the same concept done above, we will solve.
$ 27\overset{24}{\overline{\left){\begin{align}
& 675 \\
& 54\downarrow \\
& \overline{\text{135}} \\
& 132 \\
& \overline{\text{ }3} \\
\end{align}}\right.}} $
Now, we will take divisor 27 as dividend and remainder 3 to be divisor. We get as
$ 3\overset{9}{\overline{\left){\begin{align}
& 27 \\
& 27 \\
& \overline{\text{ }0} \\
\end{align}}\right.}} $
Thus, we can now say that divisor 3 is HCF of 567, 621, 675.
Thus, $ HCF\left( 567,621,675 \right) $ is 3.
Note: Do not assume a successive division method to be the same as normal division we do in prime factorization. Though the answer will be correct, the method of solving will be wrong. So, students should be clear with the methods of finding the highest common factor and then solve as per asked in question.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
How do you graph the function fx 4x class 9 maths CBSE
Which are the Top 10 Largest Countries of the World?
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
The largest tea producing country in the world is A class 10 social science CBSE
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE