Question 3 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 4 :
Fundamental theorem of arithmetic is also called as ______ Factorization Theorem.
Question 5 :
Find HCF of <span class="MathJax_Preview"></span><span class="MathJax"><span class="math"><span><span><span class="mrow"><span class="mn">25 and 55:</span></span><span></span></span></span><span></span></span><span class="MJX_Assistive_MathML">25 and </span></span>
Question 10 :
To get the terminating decimal expansion of a rational number $\dfrac{p}{q}$. if $q = 2^m 5^n$ then $m$ and $n$ must belong to .................
Question 13 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 14 :
Let $x$ be an irrational number then what can be said about ${x}^{2}$
Question 16 : <span>Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion</span><div><span>$\displaystyle \frac{7}{210}$</span></div>
Question 22 : <span>Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion</span><div><span>$\displaystyle \frac{15}{1600}$</span></div>
Question 24 :
Euclids division lemma, the general equation can be represented as .......
Question 26 :
Let $x=\dfrac { p }{ q } $ be a rational number, such that the prime factorization of $q$ is of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which terminates.
Question 27 :
<span>$2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to</span>
Question 29 :
According to Euclid's division algorithm, HCF of any two positive integers $a$ and $b$ with $a > b$ is obtained by applying Euclid's division lemma to $a$ and $b$ to find $q$ and $r$ such that $a = bq + r$, where $r$ must satisfy<br/>
Question 30 :
The decimal representation of $\dfrac { 93 }{ 1500 }$ will be
Question 33 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 36 :
The rational number which can be expressed as a terminating decimal is:
Question 38 :
We need blocks to build a building. In the same way _______ are the basic blocks to form all natural numbers.
Question 39 :
Using fundamental theorem of Arithmetic find L.C.M. and H.C.F of $816$ and $170$.
Question 40 :
Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.<br/>$\dfrac { 13 }{ 3125 } $
Question 43 :
Write whether every positive integer can be of the form $4q + 2$, where $q$ is an integer.<br/>
Question 45 :
$\dfrac {1}{2} = 0.5$<br/>It is a terminating decimal because the denominator has a factor as ...........<br/>
Question 46 :
A real number $\displaystyle \frac{2^2 \times 3^2 \times 7^2}{2^5 \times 5^3 \times 3^2 \times 7}$ will have _________.
Question 47 :
The product of a non-zero rational and an irrational number is<br>
Question 48 :
If we apply Euclid"s division algorithm for $20$ using $ 8$ then the correct answer will be:
Question 49 :
Three ropes are $7\ m, 12\ m\ 95\ cm$ and $3\ m\ 85\ cm$ long. What is the greatest possible length that can be used to measure these ropes?
Question 51 :
Choose the correct alternative answer for the question given below.<br>Decimal expansion of which of the following is non-terminating recurring?
Question 52 :
If the H.C.F. of $A$ and $B$ is $24$ and that of $C$ and $D$ is $56,$ then the H.C.F. of $A, B, C$ and $D$ is
Question 53 :
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is
Question 54 :
If the denominator of a fraction has only factors of $2$ and factors of $5$, the decimal expression .............
Question 56 :
<span>Use Euclid's division lemma to find the HCF of $40$</span> and $248$.
Question 57 :
If any positive even integer is of the form $4q$ or $4q + 2$, then $q$ belongs to:<br/>
Question 58 :
In the decimal expansion of rational number $ \dfrac{43}{{2}^{2} \times {5}^{3}} $, after how many digits decimal will end ?
Question 59 :
There are five odd numbers $1, 3, 5, 7, 9$. What is the HCF of these odd numbers?
Question 61 :
Euclids division lemma states that if a and b are any two $+$ ve integers, then there exists unique integers q and r such that :<br>
Question 63 :
If HCF of $210$ and $55$ is of the form $(210) (5) + 55 y$, then the value of $y$ is :<br/>
Question 64 :
The H. C. F. of $252$, $324$ and $594$ is ____________.
Question 65 :
The greatest integer that divides $358,\ 376$ and $ 232$. The same remainder in each case is
Question 66 :
According to Euclid's division algorithm, using Euclid's division lemma for any two positive integers $a$ and $b$ with $a > b$ enables us to find the<br/>
Question 69 :
If $\displaystyle d=\frac { 1 }{ { 2 }^{ 3 }\times { 5 }^{ 7 } } $ is expressed as a terminating decimal, <span>how many non zero digits will $d$ have?<br/></span>
Question 73 :
When the HCF of $468$ and $222$ is written in the form of  $ 468 x + 222y$ then the value of $ x$ and $y$ is 
Question 74 : <span>Use Euclid's division lemma to find the HCF of the following</span><div><br/></div><div>16 and 176</div>
Question 75 :
The decimal expansion of the rational number $\displaystyle\frac{23}{2^{3}5^{2}}$, will terminate after how many places of decimal?
Question 76 :
The decimal expansion of the rational number $\dfrac {33}{2^2\cdot 5}$ will terminate after:<br/>
Question 77 :
Find HCF of $70$ and $245$ using Fundamental Theorem of Arithmetic. 
Question 80 :
For finding the greatest common divisor of two given integers. A method based on the division algorithm is used called ............
Question 83 :
Mark the correct alternative of the following.<br>The HCF of $100$ and $101$ is _________.<br>
Question 84 :
If $d$ is the $HCF$ of 45 and 27, then $x, y$ satisfying $d=27x+45y$ are :
