Answer

Verified

390.3k+ views

**Hint:**We have to solve this type of question with the concept of factorisation. We have to find the factors of 1008. Write it in a single expression and look for the single digit number which is not paired. Thus, that number is the required answer.

**Complete step by step solution:**

According to the question, we are asked to find the single digit number which on dividing with 1008 gives a perfect square.

We have been given the number 1008.

We have to first find the factors of 1008.

Let us find the factors of 1008.

Factoring is a method where we can find the factor of a number by dividing the given number by divisible prime number.

By the factoring method, we get

\[\begin{align}

& 2\left| \!{\underline {\,

1008 \,}} \right. \\

& 2\left| \!{\underline {\,

504 \,}} \right. \\

& 2\left| \!{\underline {\,

252 \,}} \right. \\

& 2\left| \!{\underline {\,

126 \,}} \right. \\

& 3\left| \!{\underline {\,

63 \,}} \right. \\

& 3\left| \!{\underline {\,

21 \,}} \right. \\

& 7\left| \!{\underline {\,

7 \,}} \right. \\

& 1\left| \!{\underline {\,

1 \,}} \right. \\

\end{align}\]

Now, we get the factors of 1008 which are 2, 2, 2, 2, 3, 3 and 7.

So we can write 1008 as

\[1008=2\times 2\times 2\times 2\times 3\times 3\times 7\]

Here, we have to look for the pair of terms.

There are two pairs of 2 and one pair of 3.

But we observe that the number 7 is not having a pair.

Hence, on dividing the given number by 7, we should get a perfect square.

We know that \[144\times 7\] is equal to 1008.

\[\Rightarrow \dfrac{1008}{7}=\dfrac{144\times 7}{7}\]

On cancelling 7 from the numerator and denominator of the right-hand side of the equation, we get

\[\dfrac{1008}{7}=144\]

But we know that \[144={{12}^{2}}\].

On taking the square root of 144, we get

\[\sqrt{144}=\sqrt{{{12}^{2}}}\]

Using the property \[\sqrt{{{x}^{2}}}=x\], we get

\[\sqrt{144}=12\]

12 is the perfect square root of 144.

Hence, on dividing the given number by 7, we get a perfect square.

**Therefore, 1008 divided by the single digit number 7 gives a perfect square.**

**Note:**We can also solve this question by trial and error method. Take the entire digit from 1 to 9 and divide with the given number. Check for which number on dividing with 1008, we get a perfect square.

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?

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

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

Differentiate between homogeneous and heterogeneous class 12 chemistry 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

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

What organs are located on the left side of your body class 11 biology CBSE