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CBSE Questions for Class 6 Maths Playing With Numbers Quiz 5 - MCQExams.com
CBSE
Class 6 Maths
Playing With Numbers
Quiz 5
What is the value of $$x$$ for which $$x, x + 1, x + 3$$ are all prime numbers?
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$$0$$
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$$1$$
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$$2$$
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$$101$$
Explanation
Option $$A :$$ Substitute $$x=0,$$
$$x,x+1,x+3=0,1,3$$ are not prime numbers.
Option $$B :$$ Substitute $$x=1,$$
$$x,x+1,x+3=1,2,4$$ are not prime numbers.
Option $$C :$$ Substitute $$x=2,$$
$$x, x + 1, x + 3=2,3,5$$ which are all prime numbers.
Hence, option $$C$$ is correct.
The smallest 3 digit prime number is:
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$$101$$
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$$103$$
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$$109$$
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$$113$$
Explanation
The smallest 3-digit number is $$100$$, which is divisible by $$2$$.
$$\therefore$$ $$100$$ is not a prime number.
$$\sqrt{100}< 11$$ and $$101$$ is not divisible by any of the prime numbers $$2,3,5,7,11$$.
$$\therefore$$ $$101$$ is a prime number.
Hence $$101$$ is the smallest 3-digit prime number.
Which of the following number is a prime?
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$$667$$
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$$861$$
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$$481$$
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$$331$$
Explanation
$$667$$ is divisible by $$23$$
$$861$$ is divisible by $$3$$
$$481$$ is divisible by $$13$$
$$331$$ is divisible only by $$1$$ and $$331$$.
$$\therefore 331$$ is a prime number.
Which of the following is a prime number?
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$$33$$
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$$81$$
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$$93$$
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$$97$$
Explanation
Clearly, $$97$$ is a prime number.
Consider the following numbers.
$$247$$
$$203$$
Which of the above number is/are prime?
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$$1$$ only
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$$2$$ only
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Both $$1$$ and $$2$$
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Neither $$1$$ nor $$2$$
Explanation
A number which is divisible by itself and $$1$$ are prime numbers.
1. $$247 = 13\times 19$$
2. $$203 = 7\times 79$$
Here both the numbers have some divisors.
So, none of the two are prime.
Which one of the following is a prime number?
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$$184$$
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$$171$$
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$$173$$
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$$221$$
Explanation
$$184 = 23\times 8$$
Therefore, cannot be prime
$$171 = 19\times 9$$
Therefore,cannot be prime
$$221 = 17\times 13$$
Therefore, cannot be prime
Hence, by elimination we have $$173$$ as a prime number.
Which one of the following is not a prime number?
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$$31$$
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$$61$$
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$$71$$
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$$91$$
Explanation
$$91$$ is divisible by $$7$$ and $$13$$. So, it is not a prime number.
Rest all the given numbers are prime numbers since they don't have any factors other than $$1$$ and themselves.
Find $$HCF$$ by finding factors:
$$16$$ and $$56$$.
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$$6$$
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$$18$$
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$$8$$
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$$9$$
Explanation
The given numbers are $$16$$ and $$56$$
Factorizing the given numbers,
$$16 = 2 \times 2 \times 2 \times 2$$
$$56 = 2 \times 2 \times 2 \times 7$$
Since, the common factors are $$2,2,2$$, this implies that
$$H.C.F = 2 \times 2 \times 2$$
$$=8$$
Hence, the correct option is $$Op-C$$.
Find HCF of $$66$$ and $$88$$.
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$$21$$
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$$23$$
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$$24$$
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$$22$$
Explanation
Factorization of the following
$$66 = 1 \times 3 \times 2 \times 11$$
$$88 = 1 \times 2 \times 2 \times 2 \times 11$$
Since, the common factor is $$1,2,11$$ this implies that
$$HCF=22$$
Hince, the correct option $$D$$
Find HCF of $$54, 81$$ and $$99$$.
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0%
$$8$$
0%
$$9$$
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$$10$$
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$$11$$
Explanation
Factorization of the following.
$$54 = 2 \times 3 \times 3 \times 3$$
$$81 = 3 \times 3 \times 3 \times 3$$
$$99 = 3 \times 3 \times 11$$
Since, the common factor is $$3 \times 3$$,this implies that
$$H.C.F = 3 \times 3$$
Hence,the correct option $$B$$.
HCF of two co-prime number is _______.
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$$1$$
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$$0$$
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$$2$$
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None of these
Explanation
HCF of two co-prime numbers is $$1$$ because they have only $$1$$ as a common factor.
HCF of two or more prime numbers is ___________.
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$$0$$
0%
$$2$$
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$$4$$
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$$1$$
Explanation
HCF of two or more prime numbers is $$1$$
Let us take an example,
$$5$$ and $$7$$ both are prime numbers.
$$5=1\times5$$
$$7=1\times7$$
So, HCF$$=1$$
Hence, $$Op-D$$ is correct.
Which of the following numbers is prime?
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$$119$$
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$$187$$
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$$247$$
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$$179$$
Explanation
$$119$$ is divisible by $$7$$
$$187$$ is divissible by $$11$$
$$247$$ is divisible by $$13$$
Bt $$179$$ is not divisible by any number.
Hence $$179$$ is a prime number.
$$( 7 \times 11 \times 13 + 13 )$$ is a/an
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Composite number
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Prime number
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Irrational number
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Imaginary number.
Explanation
$$(7\times 11\times 13+13)=13\{(7\times11)+1\}=13\times 78=1014$$
Since, $$1014$$ is divided by $$13,78$$ which is other than $$1$$ and the number itself, so it is a composite number.
The co-prime numbers from the following pairs, are ______.
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7 and 63
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36 and 25
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35 and 29
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63 and 81
Explanation
If the H.C.F of two numbers are $$1$$ they are said to be co-prime
(A) HCF (7, 63) = 7
(B) HCF (36, 25) = 1
(C) HCF (35, 29) = 1
(D) HCF (63, 81) = 9
So, 36 & 25 and 35 & 29 are co-prime numbers.
G.C.D of $$4$$ and $$19$$ is _________.
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$$1$$
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$$4$$
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$$19$$
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$$76$$
Explanation
There is no common factor between $$4$$ and $$19$$. Hence, G.C.D. of $$4$$ and $$19$$ is $$1$$.
The reciprocal of the smallest prime number is _______.
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$$0$$
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$$\dfrac {1}{2}$$
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$$1$$
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$$2$$
Explanation
Prime no. are those which has only two factors.
One and the number itself.
$$Note:$$ $$1$$ is neither prime nor composite.
So, the smallest prime number is $$2$$.
Hence, reciprocal of $$2$$ $$= \dfrac{1}{2}$$
Which of the following is not a prime number?
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$$23$$
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$$29$$
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$$43$$
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$$21$$
Explanation
Factors of $$23 = 23 \times 1$$
Factors of
$$29 = 29 \times 1 $$
Factors of
$$43 = 43 \times 1$$
Factors of
$$21 = 3 \times 7$$
So, ioption D $$23$$ is not a prime number
The number $$111111111$$ is a
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Prime number
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Composite number
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Divisible by $$\frac{10^7-1}{9}$$
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None of these
Explanation
A whole number that can be divided exactly by numbers other than 1 or itself is known as composite numbers.
111111111 is an odd composite number. It is composed of three distinct prime numbers multiplied together.
Prime factorisation of $$111111111 = {3}^{2} \times 37 \times 333667$$
Which of the following numbers are co-prime?
a) $$18$$ and $$35$$
b) $$15$$ and $$37$$
c) $$30$$ and $$415$$
d) $$17$$ and $$68$$
e) $$216$$ and $$215$$
f) $$81$$ and $$16$$
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a,b and f
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a,b,e and f
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ab,c and f
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b,d and f
Explanation
Two numbers are co-prime, if the only positive integer that divides both of them is $$1$$. That is, their H.C.F. $$=1$$
(a)
$$18=1\times 2\times 3\times 3$$
$$35=1\times 5\times 7$$
$$H.C.F.=1$$
So, the numbers are co-prime.
(b)
$$15=1\times 3\times 5$$
$$37=1\times 37$$
$$H.C.F.=1$$
So, the numbers are co-prime.
(c)
$$30=1\times 2\times 3\times 5$$
$$415=1\times 5\times 83$$
$$H.C.F.=5$$
So, the numbers are not co-prime.
(d)
$$17=1\times 17$$
$$68=1\times 2\times 2\times 17$$
$$H.C.F.=17$$
So, the numbers are not co-prime.
(e)
$$216=1\times 2\times 2\times 2\times 3\times 3\times 3$$
$$215=1\times 5\times 43$$
$$H.C.F.=1$$
So, the numbers are co-prime.
(f)
$$16=1\times 2\times 2\times 2\times 2$$
$$81=1\times 3\times 3\times 3\times 3$$
$$H.C.F.=1$$
So, the numbers are co-prime.
The total number of factors for $$50$$ are
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$$16$$
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$$6$$
0%
$$4$$
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$$10$$
Explanation
No. of factors for $$50$$
$$50=5\times 5\times 2=5^2\times 2^1$$
Total no. of factors are $$=(2+1)\times (1+1)=6$$
How many two-digit prime numbers are there having the digit $$3$$ in their units place?
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$$10$$
0%
$$8$$
0%
$$6$$
0%
$$5$$
Explanation
$$2$$ digit prime nos. having $$3$$ in their units place are-
$$13,23,43,53,73$$
$$\therefore$$ There are $$5$$ such nos.
The factor of 252 is:
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0%
2
0%
5
0%
11
0%
10
Explanation
$$252 = 2 \times 2 \times 3 \times 3 \times 7$$.
The prime factors of $$252$$ are $$2,3,7$$.
Thus the answer will be A.
A number is divisible by $$9$$, if the sum of the digits of the number is divisible by _______ .
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$$3$$
0%
$$9$$
0%
$$6$$
0%
$$2$$
Explanation
A number is divisible by 9 if the sum of the digits of the number is divisible by
9
.
For example $$ 81 $$ is divisible by $$ 9 $$ as $$ 8 + 1 = 9 $$ is divisible by $$ 9 $$.
So, option B is correct.
A student was asked to find the sum of all the prime numbers between $$10$$ and $$40.$$He found the sum as $$180.$$Which of the following statements is true?
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He missed one prime number between $$10$$ and $$20$$
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He missed one prime number between $$20$$ and $$30$$
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He added one extra prime number between $$10$$ and $$20$$
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None of these
Explanation
Prime numbers between $$10$$ and $$40$$ are $$11,13,17,19,23,29,31,37$$
Sum of these prime numbers $$= 180$$
$$\therefore$$ Option $$D$$ is correct.
Which of the following is divisible by $$9$$?
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$$75636$$
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$$89321$$
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$$75637$$
0%
$$75632$$
Explanation
Number are divisible by $$9 $$ if sum of the all the digits present in it , is divisible by $$9 $$.
$$(a)75636$$
$$\Rightarrow 7+5+6+3+6=27$$ and $$27 $$ is divisible by 9.
Hence, $$75636 $$ is divisible by $$9 $$
$$(b)89321$$
$$\Rightarrow 8+9+3+2+1=23$$ and $$23 $$ is not divisible by $$9 $$.
So, $$ 89321 $$ is not divisible by $$9 $$.
$$(c)75637$$
$$\Rightarrow 7+5+6+3+7=28$$ and $$28 $$ is not divisible by $$9 $$.
So, $$75637 $$ is not divisible by $$9 $$.
$$(c)75632$$
$$\Rightarrow 7+5+6+3+2=26$$ and $$26 $$ is not divisible by $$9 $$.
So, $$75632 $$ is not divisible by $$9 $$
Which of the following number is divisible by $$6$$?
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$$3792$$
0%
$$5634$$
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$$9832$$
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$$3684$$
Explanation
The sum of the digits of the number should be divisible by $$3$$ and the number should be even.
For option A:
$$3 + 7+ 9+ 2 =21$$ which is divisible by $$3$$ and number is even. so answer A is right.
The sum of prime numbers, out of the numbers $$17, 8, 21, 13, 41, 2, 27, 31, 51$$ is:
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$$125$$
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$$102$$
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$$104$$
0%
$$155$$
Explanation
Prime numbers out of $$17,8,21,13,41,2,27,31,51$$ are $$17,13,41,2,31$$.
Sum of prime numbers $$= 17+13+41+2+31=104$$.
Which of the following numbers is divisible by $$9$$?
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$$8576901$$
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$$96345210$$
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$$67594310$$
0%
none of these
Explanation
We use a rule to check whether the number is divisible by 9 or not.
A number is divisible by 9 if the sum of the digits is evenly divisible by 9.
Since sum of its digits $$ = 8 + 5 + 7 + 6 + 9 + 0 + 1 = 36$$
$$36$$ is divisible by $$9$$
Option (a) is the correct answer
Which of the following numbers is divisible by $$ 9 $$ ?
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$$ 972063 $$
0%
$$ 730542 $$
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$$ 785423 $$
0%
$$ 561284 $$
Explanation
We use a rule to check whether the number is divisible by 9 or not.
A number is divisible by 9 if the sum of the digits is evenly divisible by 9.
Sum of digits $$ = 9 + 7 + 2 + 0 + 3 = 27 $$ which is divisible by $$ 9 $$
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