Answer

Verified

390.3k+ views

**Hint:**By the Euclid’s algorithm, we need to divide the greater number $1032$ by the smaller number $408$ to get the values of the remainder. Then the previous divisor $408$ will become the new dividend and the remainder obtained will become the new divisor and the second division will be carried out. This process will be repeated till the value of the remainder becomes equal to zero. And the final HCF will be equal to the last non zero remainder.

**Complete step by step solution:**

By Euclid’s algorithm, we need to write the greater number $1032$ in terms of the smaller number $408$ as

$\Rightarrow 1032=408q+r$

So we need to divide $1032$ by $408$ as below.

\[408\overset{2}{\overline{\left){\begin{align}

& 1032 \\

& \underline{816} \\

& \underline{216} \\

\end{align}}\right.}}\]

So we got the quotient as $2$ and the remainder as $216$. So from the above equation we can write

$\Rightarrow 1032=408\times 2+216$

Now, the divisor $408$ will become the new dividend and the remainder $216$ will become the new divisor so that we can write

$\Rightarrow 408=216q+r$

So we divide $408$ by $216$.

\[216\overset{1}{\overline{\left){\begin{align}

& 408 \\

& \underline{216} \\

& \underline{192} \\

\end{align}}\right.}}\]

$\Rightarrow 408=216\times 1+192$

Similarly, we will divide $216$ by $192$.

\[192\overset{1}{\overline{\left){\begin{align}

& 216 \\

& \underline{192} \\

& \underline{24} \\

\end{align}}\right.}}\]

$\Rightarrow 216=192\times 1+24$

\[24\overset{8}{\overline{\left){\begin{align}

& 192 \\

& \underline{192} \\

& \underline{0} \\

\end{align}}\right.}}\]

$\Rightarrow 192=24\times 8+0$

So finally we obtained the remainder as zero. By Euclid's algorithm, the HCF of the given numbers will be equal to the last non zero remainder obtained. From above, we can see that the last non zero remainder is equal to $24$.

**Hence, the remainder of $408$ and $1032$ is equal to $24$.**

**Note:**We can find the HCF of the given two numbers using the prime factorization method too. But Euclid's algorithm is much easier. But we must carefully do all the divisions because if any intermediate division is performed incorrectly, then ultimately it will lead us to the incorrect answer. So if possible, confirm the value of HCF obtained using the prime factorization method.

Recently Updated Pages

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

Advantages and disadvantages of science

10 examples of friction in our daily life

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Who was the first to raise the slogan Inquilab Zindabad class 8 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

One cusec is equal to how many liters class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

A resolution declaring Purna Swaraj was passed in the class 8 social science CBSE